 |
A positive-definite ternary quadratic form does not represent all positive integers, Integers 17 (2017), #A41. (with Greg Doyle) |
|
Infinite products with coefficients which vanish on certain arithmetic progressions, International Journal of Number Theory 13(5) (2017), 1095-1117. (with Ayse Alaca, Saban Alaca and Zafer Selcuk Aygin) |
|
Some arithmetic convolution identities, Ramanujan Journal 43 (2017), 197-213. |
|
A class of subsums of Euler's sum, Analysis 36(4) (2016), 231-243. |
|
Representation numbers of certain quaternary quadratic forms in a genus consisting of a single class, International Journal of Number Theory 12(6) (2016), 1529-1573. (with Ayse Alaca and Saban Alaca) |
|
Bounds for the representations of integers by positive quadratic forms, Mathematics Magazine 89(2) (2016), 122-131. |
|
Quartic residuacity and the quadratic character of certain quadratic irrationalities, International Journal of Number Theory 11(8) (2015), 2487-2503. (with Ronald J. Evans) |
|
Ternary quadratic forms and eta quotients, Canadian Mathematical Bulletin 58(4) (2015), 858-868. |
|
Some new evaluations of the Legendre symbol (a+bsqrt(q)/p), Acta Arithmetica 170(4) (2015), 361-380. (with Lerna Pehlivan) |
|
A "four integers" theorem and a "five integers" theorem, American Mathematical Monthly 122(6) (2015), 528-536. |
|
Historical remark on Ramanujan's tau function, American Mathematical Monthly 122(1) (2015), 30-35. |
|
Historical remark on a theorem of Zhang and Yue, Journal of Number Theory 147 (2015), 691-693. |
|
Double Gauss sums, Journal of Combinatorics and Number Theory 6(2) (2014), 127-153. (with Ayse Alaca and Saban Alaca) |
|
Ternary quadratic forms ax2+by2+cz2 representing all positive integers 8k+4, Acta Arithmetica 166(4) (2014), 391-396. |
|
On the number of representations of a positive integer as a sum of two binary quadratic forms, International Journal of Number Theory 10(6) (2014), 1395-1420. (with Saban Alaca and Lerna Pehlivan) |
|
Analogues of Ramanujan's 24 squares formula, International Journal of Number Theory 10(5) (2014), 1099-1119. (with Faruk Uygul) |
|
The power series expansion of certain infinite products, Ramanujan Journal 33 (2014), 23-53. (with Lerna Pehlivan) |
|
Euler products in Ramanujan's lost notebook, International Journal of Number Theory 9(5) (2013), 1313-1349. (with Bruce C. Berndt and Byungchan Kim) |
|
The parents of Jacobi's four squares theorem are unique, American Mathematical Monthly 120(4) (2013), 329-345. |
|
Quadratic forms and a product-to-sum formula, Acta Arithmetica 158(1) (2013), 79-97. |
|
On the quaternary forms x2+y2+2z2+3t2, x2+2y2+2z2+6t2, x2+3y2+3z2+6t2 and 2x2+3y2+6z2+6t2, International Journal of Number Theory 8(7) (2012), 1661-1686. (with A. Alaca) |
|
Some product-to-sum identities, Journal of Combinatorics and Number Theory 4(1) (2012), 35-52. (with S. Alaca and L. Pehlivan) |
|
Some arithmetic identities involving divisor functions, Functiones et Approximatio 46(2) (2012), 261-271. (with S. Alaca and F. Uygul) |
|
Fourier series of a class of eta quotients, International Journal of Number Theory 8(4) (2012), 993-1004. |
|
Lifting monogenic cubic fields to monogenic sextic fields, Kodai Mathematical Journal 34 (2011), 410-425. (with M. J. Lavallee and B. K. Spearman) |
|
Restricted Eisenstein series and certain convolution sums, Journal of Combinatorics and Number Theory 3(1) (2011), 1-14. (with A. Alaca, S. Alaca and F. Uygul) |
|
The number of representations of a positive integer by certain octonary quadratic forms, Functiones et Approximatio 43 (2010), 45-54. (with S. Alaca) |
|
Sextenary quadratic forms and an identity of Klein and Fricke, International Journal of Number Theory 6 (2010), 169-183. (with A. Alaca and S. Alaca) |
|
Fourteen octonary quadratic forms, International Journal of Number Theory 6 (2010), 37-50. (with A. Alaca and S. Alaca) |
|
Representations by sextenary quadratic forms whose coefficients are 1, 2 and 4, Acta Arithmetica 141 (2010), 289-309. (with A. Alaca, S. Alaca and F. Uygul) |
|
Sums of 4k squares: a polynomial approach, Journal of Combinatorics and Number Theory 1(2) (2009), 33-52. (with A. Alaca and S. Alaca) |
|
Some infinite products of Ramanujan type, Canadian Mathematical Bulletin 52 (2009), 481-492. (with A. Alaca and S. Alaca) |
|
Evaluation of the sums Σm=a (mod 4)σ(m)σ(n-m), Czechoslovak Mathematical Journal 59 (2009), 847-859. (with A. Alaca and S. Alaca) |
|
Some identities involving theta functions, Journal of Number Theory 129 (2009), 1404-1431. (with A. Alaca and S. Alaca) |
|
Some new theta function identities with applications to sextenary quadratic forms, Journal of Combinatorics and Number Theory 1 (2009), 89-98. (with A. Alaca and S. Alaca) |
|
The number of representations of a positive integer by certain quaternary quadratic forms, International Journal of Number Theory 5 (2009), 13-40. (with A. Alaca, S. Alaca and M. F. Lemire) |
|
A normal relative integral basis for the normal closure of a pure cubic field over Q(√-3), International Journal of Contemporary Mathematical Sciences 3 (2008), 1427-1432. (with B. K. Spearman) |
|
Seven octonary quadratic forms, Acta Arithmetica 135 (2008), 339-350. (with A. Alaca and S. Alaca) |
|
Arithmetic progressions and binary quadratic forms, American Mathematical Monthly 115 (2008), 252-254. (with A. Alaca and S. Alaca) |
|
Liouville's sextenary quadratic forms x2+y2+z2+t2+2u2+2v2, x2+y2+2z2+2t2+2u2+2v2 and x2+2y2+2z2+2t2+2u2+4v2, Far East Journal of Mathematical Sciences 30 (2008), 547-556.(with A. Alaca and S. Alaca) |
|
Indices of integers in cyclic cubic fields, International Mathematical Forum 3 (2008), 1595-1606.(with B. K. Spearman) |
|
Berndt's curious formula, International Journal of Number Theory 4 (2008), 677-689.(with A. Alaca and S. Alaca) |
|
The simplest D4-octics, International Journal of Algebra 2 (2008), 79-89.(with B. K. Spearman) |
|
On the representations of a positive integer by the forms x2+y2+z2+2t2 and x2+2y2+2z2+2t2, International Journal of Modern Mathematics 3 (2008), 225-230. |
|
On Liouville's twelve squares theorem, Far East Journal of Mathematical Sciences 29 (2008), 239-242. |
|
Theta function identities and representations by certain quaternary quadratic forms II, International Mathematical Forum 3 (2008), 539-579. (with A. Alaca, S. Alaca and M. F. Lemire) |
|
The convolution sum Σl+16m=nσ(l)σ(m), Canadian Mathematical Bulletin 51 (2008), 3-14. (with A. Alaca and S. Alaca) |
|
Theta function identities and representations by certain quaternary quadratic forms, Int. J. Number Theory 4 (2008), 219-239. (with A. Alaca, S. Alaca and M. F. Lemire) |
|
A number field with infinitely many normal integral bases, Fibonacci Quarterly 45 (2007), 151-154. (with D. Eloff and B. K. Spearman) |
|
The conductor of Lecacheux's parametric family of cyclic quintic fields, Indian Journal of Pure and Applied Mathematics 38 (2007), 231-240. (with A. K. Silvester and B. K. Spearman) |
|
A4-sextic fields with a power basis, Missouri Journal of Mathematical Sciences 19 (2007), 188-194. (with D. Eloff and B. K. Spearman) |
|
Nineteen quaternary quadratic forms, Acta Arithmetica 130 (2007), 277-310. (with A. Alaca, S. Alaca and M. F. Lemire) |
|
On the common index divisors of a dihedral field of prime degree, Int. J. Math. Math. Sci. 2007 (2007), 1-8. (with B.K. Spearman and Q. Yang) |
|
The simplest proof of Jacobi's six squares theorem, Far East J. Math. Sci. 27 (2007), 187-192. (with A. Alaca and S. Alaca) |
|
On the quaternary forms x2+y2+z2+5t2, x2+y2+5z2+5t2 and x2+5y2+5z2+5t2, JP J. Algebra Number Theory Appl. 9 (2007), 37-53. (with A. Alaca and S. Alaca) |
|
Jacobi's identity and representation of integers by certain quaternary quadratic forms, Int. J. Modern Math. 2 (2007), 143-176. (with A. Alaca, S. Alaca and M. F. Lemire) |
|
Evaluation of the convolution sums Σl+24m=nσ(l)σ(m) and Σ3l+8m=nσ(l)σ(m), Math. J. Okayama Univ. 49 (2007), 93-111. (with A. Alaca and S. Alaca) |
|
On integers with prime factors restricted to certain congruence classes, Far East J. Math. Sci. 24 (2007), 153-161. (with B. K. Spearman) |
|
Lambert series and Liouville's identities, Dissertationes Math. 445 (2007), 1-72. (with A. Alaca, S. Alaca and E. McAfee) |
|
An infinite class of identities, Bull. Austral. Math. Soc. 75 (2007), 239-246. (with A. Alaca and S. Alaca) |
|
Evaluation of the convolution sums Σl+6m=nσ(l)σ(m) and Σ2l+3m=nσ(l)σ(m), J. Number Theory 124 (2007), 491-510. (with S. Alaca) |
|
Reducibility and the Galois group of a parametric family of quintic polynomials, Missouri J. Math. Sci. 19 (2007), 2-10. (with M. J. Lavallee and B. K. Spearman) |
|
Nonexistence of a composition law, Math Mag. 80 (2007), 142-144. (with S. Alaca) |
|
Evaluation of the convolution sums Σl+18m=nσ(l)σ(m) and Σ2l+9m=nσ(l)σ(m), International Mathematical Forum 2 (2007), 45-68. (with A. Alaca and S. Alaca) |
|
The convolution sum Σl+8m=nσ(l)σ(m), Pacific J. Math. 228 (2006), 387-396. |
|
On a double series of Chan and Ong, Georgian Math. J. 13 (2006), 793-805. |
|
Evaluation of complete elliptic integrals of the first kind at singular moduli, Taiwanese J. Math. 10 (2006), 1633-1660. (with H. Muzaffar) |
|
Integral bases for an infinite family of cyclic quintic fields, Asian J. Math. 10 (2006), 765-772. (with D. Eloff and B. K. Spearman) |
|
The prime ideal factorization of 2 in pure quartic fields with index 2, Math. J. Okayama Univ. 48 (2006), 43-46. (with B. K. Spearman) |
|
The proportion of cyclic quartic field discriminants divisible by a given prime, Kobe J. Math. 23 (2006), 1-10. (with B. K. Spearman) |
|
Values of the Euler phi function not divisible by a given prime, Kobe J. Math. 23 (2006), 1-10. (with B. K. Spearman) |
|
An arithmetic formula of Liouville, J. Théor. Nombres Bordeaux 18 (2006), 223-239. (with E. McAfee) |
|
On the two-dimensional theta functions of the Borweins, Acta Arith. 124 (2006), 177-195. (with A. Alaca and S. Alaca) |
|
Cyclic cubic fields of given conductor and given index, Canad. Math. Bull. 49 (2006), 472-480. (with A. K. Silvester and B. K. Spearman) |
|
Explicit decomposition of a rational prime in a cubic field, Int. J. Math. Math. Sci. 2006 (2006), 1-11. (with S. Alaca and B. K. Spearman) |
|
On the distribution of cyclic cubic fields with index 2, Int. J. Number Theory 2 (2006), 235-247. (with B. K. Spearman) |
|
Evaluation of the convolution sums ∑ l+12m=n σ(l)σ(m) and ∑ 3l+4m=n σ(l)σ(m), Advances in Theoretical and Applied Mathemeatics 1 (2006), 27-48. (with A. Alaca and S. Alaca) |
|
Cyclic quartic fields with a unique normal integral basis, Far East J. Math. Sci. 21 (2006), 235-240. (with B. K. Spearman) |
|
Ramanujan identities and Euler products for a type of Dirichlet series, Acta Arith. 122 (2006), 349-393. (with Z.-H. Sun) |
|
An arithmetic formula of Liouville type and an extension of an identity of Ramanujan, JP J. Algebra Number Theory Appl. 6 (2006), 33-56. (with E. McAfee) |
|
On the number of representations of n by ax² + bxy + cy², Acta Arith. 122 (2006), 101-171. (with Z.-H. Sun) |
|
Evaluation of two convolution sums involving the sum of divisors function, Bull. Austral. Math. Soc. 73 (2006), 107-115. (with M. Lemire) |
|
PSL(2,5) sextic fields with a power basis, Kodai Math. J. 29 (2006), 5-12. (with B. K. Spearman and A. Watanabe) |
|
Dihedral quintic fields with a power basis, Math. J. Okayama Univ. 47 (2005), 75-79. (with M. J. Lavallee, B. K. Spearman, and Q. Yang) |
|
Irreducible quartic polynomials with factorizations modulo p, Amer. Math. Monthly 112 (2005), 876-890. (with E. Driver and P. A. Leonard) |
|
Evaluation of some convolution sums involving the sum of divisors functions, Yokohama Math. J. 52 (2005), 39-57. (with N. Cheng) |
|
The convolution sum  , Int. J. Number Theory 1 (2005), 193-205. |
|
Sums of six squares, Far East J. Math. Sci. 16 (2005), 17-41. (with E. McAfee) |
|
Two term class number formulae of Dirichlet type, Far East J. Math. Sci. 16 (2005), 1-16. (with S. Godin) |
|
Tables for two term class number formulae of Dirichlet type (with S. Godin) |
|
Watson's method of solving a quintic equation, JP J. Algebra Number Theory Appl. 5 (2005), 49-73. (with M. J. Lavallee and B. K. Spearman) |
|
Sums of sixteen and twenty-four triangular numbers, Rocky Mountain J. Math. 35 (2005), 857-868. (with J. G. Huard) |
|
On the Lagrange resolvents of a dihedral quintic polynomial, Int. J. Math. Math. Sci. 69 (2004), 3817-3820. (with B. K. Spearman) |
|
A cubic transformation formula for 2F1(1/3,2/3;1;z) and some arithmetic convolution formulae, Math. Proc. Camb. Phil. Soc. 137 (2004), 519-539. |
|
The factorization of 2 in cubic fields with index 2, Far East J. Math. Sci. 14 (2004), 273-282. (with S. Alaca and B. K. Spearman) |
|
Density of integers which are discriminants of cyclic fields of odd prime degree, Arch. Math. (Basel) 83 (2004), 507-513. (with B. K. Spearman) |
|
Infinitely many insolvable Diophantine equations, Amer. Math. Monthly 111 (2004), 909-913. (with N. Kimura) |
|
Evaluation of Weber's functions at quadratic irrationalities, JP J. Algebra Number Theory Appl. 4 (2004), 209-259. (with H. Muzaffar) |
|
Convolution sums involving the divisor function, Proc. Edinburgh Math. Soc. 47 (2004), 561-572. (with N. Cheng) |
|
An extension of Vulakh's theorem on units in complex cubic fields, Far East J. Math. Sci. 14 (2004), 1-7. |
|
The proportion of cyclic quartic fields with discriminant divisible by a given prime, Proc. Japan Acad. Ser. A Math. Sci. 80 (2004), 141-145. (with B. K. Spearman) |
|
Normal integral bases for Emma Lehmer's parametric family of cyclic quintics, J. Théor. Nombres Bordeaux 16 (2004), 215-220. (with B. K. Spearman) |
|
On the number of representations of a positive integer by a binary quadratic form, Acta. Arith. 114 (2004), 87-98. (with P. Kaplan) |
|
On Voronoi's method for finding an integral basis of a cubic field, Util. Math. 65 (2004), 163-166. (with S. Alaca). |
|
p-Integral bases of a quartic field defined by a trinomial x4 + ax + b, Far East J. Math. Sci. 12 (2004), 137-168. (with S. Alaca). |
|
On real cubic fields with a unique fundamental unit, Far East J. Math. Sci. 12 (2004), 1-7. |
|
n=&Delta + &Delta + 2(&Delta + &Delta), Far East J. Math. Sci. 11 (2003), 233-240. |
|
Congruences for quadratic units of norm -1, Ramanujan J. 7 (2003), 449-453. (with R. J. Evans and P. Kaplan) |
|
A simple method for finding an integral basis of a quartic field defined by a trinomial x4+ax+b, JP J. Algebra Number Theory Appl. 3 (2003), 477-505. (with S. Alaca). |
|
The index of a cyclic quartic field, Monatsh. Math. 140 (2003), 19-70. (with B. K. Spearman) |
|
The discriminant of a cyclic field of odd prime degree, Rocky Mountain J. Math. 33 (2003), 1101-1122. (with B. K. Spearman). |
|
The 2-power degree subfields of the splitting fields of polynomials with Frobenius Galois groups, Comm. Algebra 31 (2003), 4745-4763. (with B. K. Spearman and Q. Yang) |
|
Sums of twelve squares, Acta Arith. 109 (2003), 195-204. (with J. G. Huard). |
|
A relative integral basis over Q(√-3) for the normal closure of a pure cubic field, Int. J. Math. Math. Sci. 25 (2003), 1623-1626. (with B.K. Spearman) |
|
The index of a dihedral quartic field, JP J. Algebra Number Theory Appl. 3 (2003), 121-144. (with A. K. Silvester and B. K. Spearman). |
|
Density of integers which are discriminants of cyclic cubic fields, Far East J. Math. Sci. 8 (2003), 83-87. (with B. K. Spearman) |
|
On a procedure for finding the Galois group of a quintic polynomial, Sci. Math. Jpn. 57 (2003), 187-190. (with B. K. Spearman) |
|
Elementary evaluation of certain convolution sums involving divisor functions, Number Theory for the Millennium II, edited by M. A. Bennett, B. C. Berndt, N. Boston, H. G. Diamond, A. J. Hildebrand, and W. Philipp, A. K. Peters, Natick, Massachusetts, 2002, pp. 229-274. (with J. G. Huard, Z. M. Ou, and B. K. Spearman) |
|
Remark on the infinite series , Crux Mathematicorum 28 (2002), 222. |
|
Uniquely determined unknowns in systems of linear equations, Math. Mag. 75 (2002), 53-57. (with K. Hardy and B. K. Spearman) |
|
Cubic fields with index 2, Monatsh. Math. 134 (2002), 331-336. (with B. K. Spearman) |
|
The discriminant of a dihedral quintic field defined by a trinomial x5 + ax + b, Canad. Math. Bull. 45 (2002), 138-153. (with B. K. Spearman) |
|
Commentary on an unpublished lecture by G. N. Watson on solving the quintic, Math. Intelligencer 24 (2002), 15-33. (with B. C. Berndt and B. K. Spearman) |
|
A restricted Epstein zeta function and the evaluation of some definite integrals, Acta Arith. 104 (2002), 23-66. (with H. Muzaffar) |
|
Sums of sixteen squares, Far East J. Math. Sci. 7 (2002), 147-164. (with J. G. Huard) |
|
The genera representing a positive integer, Acta Arith. 102 (2002), 353-361. (with P. Kaplan) |
|
On the density of cyclic quartic fields, Canad. Math. Bull. 44 (2001), 97-104. (with Z. M. Ou) |
|
Conditions for the insolvability of the quintic equation x5 + ax + b = 0, Far East J. Math. Sci. 3 (2001), 209-225. (with B. K. Spearman) |
|
Integers which are discriminants of bicyclic or cyclic quartic fields, JP J. Algebra Number Theory Appl. 1 (2001), 179-194. (with B.K. Spearman) |
|
On the relative sizes of A and B in p=A²+B², where p is a prime=1(mod 4), Far East J. Math. Sci. 3 (2001), 129-132. |
|
An arithmetic proof of Jacobi's eight squares theorem, Far East J. Math. Sci. 3 (2001), 1001-1005. |
|
Cubic fields with a power basis, Rocky Mountain J. Math. 31 (2001), 1103-1109. (with B. K. Spearman) |
|
Note on a paper of Kobayashi and Nakagawa, Sci. Math. Jpn. 53 (2001), 323-334. (with B. K. Spearman) |
|
The cubic congruence x³+Ax²+Bx+C = 0 (mod p) and binary quadratic forms II, J. London Math. Soc. 64 (2001), 273-274. (with B. K. Spearman) |
|
Quartic trinomials with Galois groups A4 and V4, Far East J. Math. Sci. 2 (2000), 665-672. (with B. K. Spearman) |
|
Small solutions of ϕ1x1²+&sdot&sdot&sdot+ϕnxn² =0, Canad. J. Math. 52 (2000), 613-632. (with Z. M. Ou) |
|
Pure quintic fields defined by trinomials, Rocky Mountain J. Math. 30 (2000), 371-391. (with B. K. Spearman) |
|
The simplest arithmetic proof of Jacobi's four squares theorem, Far East J. Math. Sci. 2 (2000), 433-439. (with B. K. Spearman) |
|
 and related series, Mathematical Analysis and Applications (Editor Th. M. Rassias), Hadronic Press, Inc., Florida, 1999, pp. 183-196. (with Zhang Nan-Yue) |
|
Dihedral quintic polynomials and a theorem of Galois, Indian J. Pure Appl. Math. 30 (1999), 839-845. (with B. K. Spearman) |
|
Some Lambert series expansions of products of theta functions, Ramanujan J. 3 (1999), 367-384. |
|
On a formula of Howard, Bull. Hong Kong Math. Soc. 2 (1999), 325-340. (with B. K. Spearman) |
|
Gauss' congruence from Dirichlet's class number formula and generalizations, Number Theory in Progress, Proceedings of the International Conference on Number Theory (Editors: K. Györy, H. Iwaniec and J. Urbanowicz), Zakopane, Poland, 1997, pp. 813-839, deGruyter, Berlin, 1999. (with G. J. Fox and J. Urbanowicz) |
|
Cyclic quartic subfields of the splitting field of a quintic trinomial x5 + ax + b with Galois group F20, Far East J. Math. Sci. 1 (1999), 659-667. (with B. K. Spearman) |
|
DeMoivre's quintic and a theorem of Galois, Far East J. Math. Sci. 1 (1999), 137-143. (with B. K. Spearman) |
|
Cyclic quartic fields and F20 quintics, Far East J. Math. Sci. 1 (1999), 121-126. (with B. K. Spearman) |
|
Values of the Dedekind eta function at quadratic irrationalities, Canad. J. Math. 51 (1999), 176-224. (with A. J. van der Poorten) |
|
The factorization of x5 ± xa + n, Fibonacci Quart. 36 (1998), 158-170. (with B. K. Spearman) |
|
Sarvadaman Chowla (1907-1995), Notices Amer. Math. Soc. 45 (1998), 594-598. (with R. G. Ayoub and J. G. Huard) |
|
Pascal's triangle (mod 8), European J. Combin. 19 (1998), 45-62. (with J. G. Huard and B. K. Spearman) |
|
An explicit integral basis for a pure cubic field, Far East J. Math. Sci. 6 (1998), 1-14. (with B. K. Spearman) |
|
Quadratic subfields of the splitting field of a dihedral quintic trinomial x5 + ax + b, New Zealand J. Math. 26 (1997), 293-299. (with B. K. Spearman and L. Y. Spearman) |
|
The conductor of a cyclic quartic field using Gauss sums, Czechoslovak Math. J. 47 (1997), 453-462. (with B. K. Spearman) |
|
On Pascal's triangle modulo p2, Colloq. Math. 74 (1997), 157-165. (with J. G. Huard and B. K. Spearman) |
|
Pascal's triangle (mod 9), Acta Arith. 78 (1997), 331-349. (with J. G. Huard and B. K. Spearman) |
|
On a formula of Dirichlet, Far East J. Math. Sci. 5 (1997), 153-157. (with P. Kaplan) |
|
Bernoulli's identity without calculus, Math. Mag. 70 (1997), 47-50. |
|
Normal relative integral bases for quartic fields over quadratic subfields, Kodai Math. J. 19 (1996), 293-307. (with B. K. Spearman) |
|
Discriminant of the normal closure of a dihedral quartic field, Arch. Math. (Basel) 67 (1996), 290-295. (with J. G. Huard and B. K. Spearman) |
|
The intersection of two cyclotomic extensions of a quadratic field, Kyungpook Math. J. 36 (1996), 117-124. (with B. K. Spearman) |
|
On solvable quintics X5 + aX + b and X5 + aX2 + b, Rocky Mountain J. Math. 26 (1996), 753-772. (with B. K. Spearman) |
|
Relative integral bases for quartic fields over quadratic subfields, Acta Math. Hungar. 70 (1996), 185-192. (with B. K. Spearman) |
|
On Tornheim's double series, Acta Arith. 75 (1996), 105-117. (with J. G. Huard and Zhang Nan-Yue) |
|
The conductor of a cyclic quartic field, Publ. Math. Debrecen 48 (1996), 13-43. (with B. K. Spearman) |
|
Some refinements of an algorithm of Brillhart, Number Theory, Proceedings of the Fourth Conference of the Canadian Number Theory Association, Dalhousie University, Halifax NS, July 1994, Canadian Mathematical Society Conference Proceedings 15 (1995), 409-416. |
|
An arithmetic approach to the Davenport-Hasse relation over GF(p), Rocky Mountain J. Math. 25 (1995), 1341-1350. (with J. G. Huard and B. K. Spearman) |
|
The Chowla-Selberg formula for genera, Acta Arith. 73 (1995), 271-301. (with J. G. Huard and P. Kaplan) |
|
On the set of primes p which split x3 + B modulo p, Indian J. Pure Appl. Math 26 (1995), 301-308. (with J. G. Huard and B. K. Spearman) |
|
On the Epstein zeta function, Tamkang J. Math. 26 (1995), 165-176. (with Zhang Nan-Yue) |
|
Values of the Riemann zeta function and integrals involving log(2sinhΘ/2) and log(2sinΘ/2), Pacific J. Math. 168 (1995), 271-289. (with Zhang Nan-Yue) |
|
Unramified quadratic extensions of a quadratic field, Rocky Mountain J. Math. 25 (1995), 783-788. (with B. K. Spearman) |
|
The subfields of the splitting field of a solvable quintic trinomial x5 + aX + b, J. Math. Sci. (Calcutta) 6 (1995), 15-18. (with B. K. Spearman and L. Y. Spearman) |
|
Integral bases for quartic fields with quadratic subfields, J. Number Theory 51 (1995), 87-102. (with J. G. Huard and B. K. Spearman) |
|
Predictive criteria for the representation of primes by binary quadratic forms, Acta Arith. 70 (1995), 215-278. (with J. B. Muskat and B. K. Spearman) |
|
The recurrence relation an = (An+B)an-1 + (Cn+D)an-2, Crux. Math. 20 (1994), 91-96. |
|
An elementary remark on the distribution of integers representable by a positive-definite integral binary quadratic form, Arch. Math. (Basel) 62 (1994), 38-42. (with P. Kaplan) |
|
Comparison of the lengths of the continued fractions of √D and ½(1 + √D), Proc. Amer. Math. Soc. 120 (1994), 995-1002. (with N. Buck) |
|
The primes for which an abelian cubic splits, Tokyo J. Math. 17 (1994), 467-478. (with J. G. Huard and B. K. Spearman) |
|
Evaluation of two trigonometric sums, Mathematica Slovaca 44 (1994), 575-583. (with Zhang Nan-Yue) |
|
Representation of primes by the principal form of negative discriminant D when h(D) is 4, Tamkang Journal of Mathematics 25 (1994), 321-334. (with D. Liu) |
|
Some results on the generalized Stieltjes constants, Analysis 14 (1994), 147-162. (with Zhang Nan-Yue) |
|
On finding the solutions of n=au2+buv+cv2 in integers u and v, Utilitas Math. 46 (1994), 3-19. |
|
Characterization of solvable quintics x5 + ax + b, Amer. Math. Monthly 101 (1994), 986-992. (with B. K. Spearman) |
|
A short proof of the formula for the conductor of an abelian cubic field, Norske Vid. Selsk. Skr. 2 (1994), 3-8. (with J. G. Huard and B. K. Spearman) |
|
Some infinite series involving the Riemann zeta function, in Analysis, Geometry and Groups: A Riemann Legacy Volume, Editors H. M. Srivastava and Th. M. Rassias, Hadronic Press, Palm Harbor, Florida, USA, 1993, pp. 691-712. (with Zhang Nan-Yue) |
|
A refinement of H.C. Williams' qth root algorithm, Math. Comp. 61 (1993), 475-483. (with K. Hardy) |
|
Representation of primes in arithmetic progression by binary quadratic forms, J. Number Theory 45 (1993), 61-67. (with P. Kaplan) |
|
Special values of the Lerch zeta function and the evaluation of certain integrals, Proc. Amer. Math. Soc. 119 (1993), 35-49. (with Zhang Nan-Yue) |
|
Application of the Hurwitz zeta function to the evaluation of certain integrals, Canad. Math. Bull. 36 (1993), 373-384. (with Zhang Nan-Yue) |
|
Some series representations of zeta(2n+1), Rocky Mountain J. Math. 23 (1993), 1581-1592. (with Zhang Nan-Yue) |
|
The cubic congruence x3 + Ax2 + Bx + C = 0 (mod p) and binary quadratic forms, Journal of the London Mathematical Society 46 (1992), 397-410. (with B. K. Spearman) |
|
The squareroot of an ambiguous form in the principal genus, Proc. Edinburgh Math. Soc. 36 (1992), 145-150. (with K. Hardy) |
|
The nth power of a 2 x 2 matrix, Math. Mag. 65 (1992), 336. |
|
Mathematical modelling of atom loss in delivery tubing, Canad. J. Chemistry 70 (1992), 1978-1984. (with R. S. Daniels and D. C. Wigfield) |
|
An upper bound for the sum for a certain class of functions ƒ, Proc. Amer. Math. Soc. 114 (1992), 29-35. (with E. Dobrowolski) |
|
Representing primes by binary quadratic forms, Amer. Math. Monthly 99 (1992), 423-426. (with B. K. Spearman) |
|
Determination of modulo p, Acta Arithmetica 61 (1992), 161-172. (with K. Hardy) |
|
Infrastructure des classes ambiges d'idéaux des ordres des corps quadratiques réels, Enseign. Math. 37 (1991), 263-292. (with F. Halter-Koch, P. Kaplan, and Y. Yamamoto) |
|
On Yamamoto's reciprocity law, Proc. Amer. Math. Soc. 111 (1991), 607-609. |
|
Representation of primes by the principal form of discriminant -D when the classnumber h(-D) is 3, Acta Arithmetica 57 (1991), 131-153. (with R. H. Hudson) |
|
On an assertion of Ramanujan concerning binary quadratic forms, J. Number Theory 38 (1991), 118-133. |
|
The distance between ideals in the orders of a real quadratic field, Enseign. Math. 36 (1990), 321-358. (with P. Kaplan) |
|
A deterministic algorithm for solving n = ƒu² + gv² in coprime integers u and v, Math. Comp. 55 (1990), 327-343. (with K. Hardy and J. B. Muskat) |
|
On Eisenstein's problem, Acta Arithmetica 54 (1990), 323-345. (with N. Ishii and P. Kaplan) |
|
Solving n = au2+buv+cv2 using the Euclidean algorithm, Utilitas Math. 38 (1990), 225-236. (with K. Hardy and J. B. Muskat) |
|
Evaluation of the infinite series , Proc. Amer. Math. Soc. 109 (1990), 597-603. (with K. Hardy) |
|
The integers of a cyclic quartic field, Rocky Mountain J. Math. 20 (1990), 145-150. (with R. H. Hudson) |
|
The class number of pairs of positive-definite binary quadratic forms, Acta Aritmetica 52 (1989), 103-117. (with K. Hardy) |
|
The representation of a pair of integers by a pair of positive-definite binary quadratic forms, Proc. Amer. Math. Soc. 105 (1989), 847-855. (with K. Hardy and P. Kaplan) |
|
Determination of all imaginary cyclic quartic fields with class number 2, Trans. Amer. Math. Soc. 311 (1989), 1-55. (with K. Hardy, R. H. Hudson, and D. Richman) |
|
Explicit evaluation of certain Eisenstein sums, in Number Theory, Proceedings of the First Conference of the Canadian Number Theory Association, Banff, Alberta, April 17-27, 1988, pp. 553-626, de Gruyter, Berlin, 1990. (with K. Hardy and B. K. Spearman, and the assistance of N. Buck and I. deMille) |
|
On the size of a solution of Legendre's equation, Utilitas Math. 34 (1988), 65-72. |
|
Cyclic quartic fields with relative integral bases over their quadratic subfields, Proc. Amer. Math. Soc. 103 (1988), 687-694. (with B. K. Spearman) |
|
The class number two problem for certain quartic fields, Sixteenth Manitoba Conference on Numerical Mathematics and Computing, Winnipeg, Manitoba, 1986, Congr. Numer. 56 (1987), 63-70. |
|
Calculation of the class numbers of imaginary cyclic quartic fields, Math. Comp. 49 (1987), 615-620. (with K. Hardy, R. H. Hudson, D. Richman, and N. M. Holtz) |
|
The cyclotomic numbers of order fifteen, Math. Comp. 48 (1987), 67-83. (with N. Buck, L. Smith, and B. K. Spearman) |
|
Congruences modulo 16 for the class numbers of complex quadratic fields, J. Number Theory 27 (1987), 178-195. (with K. Hardy) |
|
Cyclotomy of order twelve over GF(p²), p² ≡ 1 (mod 12), Math. Comp. 48 (1987), 444-446. (with J. B. Muskat) |
|
A congruence relating the class numbers of complex quadratic fields, Acta Arith. 47 (1986), 263-276. (with K. Hardy) |
|
Cyclotomy of order 15 over GF(p²), p=4, 11 (mod 15), Internat. J. Math. Math. Sci. 9 (1986), 665-704. (with C. Friesen, J. B. Muskat and B. K. Spearman) |
|
Cycles d'ordre au moins 16 dans le deux groupe des classes d'ideaux au sens strict de corps quadratiques, Proceedings of the International Conference on Class Numbers and Fundamental Units of Algebraic Number Fields, June 24-28, 1986, Katata, Japan, pp. 189-203, Nagoya University, Nagoya, Japan, 1986. (with P. Kaplan) |
|
The class number two problem for certain quartic fields, Proceedings of the Symposium on Algebraic Number Theory, Kyoto University, Japan, June 22-July 3, 1986, pp. 51--59. |
|
Calculation of the class numbers of certain quartic fields, Proceedings of the International Conference on Class Numbers and Fundamental Units of Algebraic Number Fields, June 24-28, 1986, Katata, Japan, pp. 139-150. |
|
Divisibilite par 16 du nombre des classes au sens strict des corps quadratiques reels dont le deux-groupe des classes est cyclique, Osaka J. Math. 23 (1986), 479-489. (with P. Kaplan and K. Hardy) |
|
On the solvability of the diophantine equation dV2 - 2eVW - dW2 = 1, Pacific J. Math. 124 (1986), 145-158. (with K. Hardy) |
|
A simple proof of Eisenstein's reciprocity law from Stickelberger's theorem, Indian J. Pure Appl. Math. 17 (1986), 169-174. (with B. K. Spearman) |
|
Another proof of Eisenstein's law of cubic reciprocity and its supplement, Rocky Mountain J. Math. 16 (1986), 395-402. (with C. Friesen and B. K. Spearman) |
|
Pell's equations x² - my² = -1, -4 and continued fractions, J. Number Theory 23 (1986), 169-182. (with P. Kaplan) |
|
A congruence for the index of a unit of a real abelian number field, Acta. Arith. 46 (1985), 57-72. (with K. Hardy) |
|
On the evaluation of the Legendre symbol (A + B√m⁄p), Acta Arith. 45 (1985), 255-272. (with K. Hardy and C. Friesen) |
|
Criteria for biquadratic residuacity modulo a prime p involving quaternary representations of p, Canad. J. Math. 37 (1985), 337-370. (with C. Friesen and L. J. Howe) |
|
Remark on the class number of Q(√2p) modulo 8 for p≡5(mod 8) a prime, Proc. Amer. Math. Soc. 93 (1985), 198-200. (with C. Friesen) |
|
An application of dihedral fields to representations of primes by binary quadratic forms, Acta Arith. 44 (1984), 407-413. (with P. Kaplan and Y. Yamamoto) |
|
Extension of a theorem of Cauchy and Jacobi, J. Number Theory 19 (1984), 309-340. (with D. A. Buell and R. H. Hudson) |
|
On the strict class number of Q(√2p) modulo 16, p≡1(mod 8) prime, Osaka J. Math. 21 (1984), 23-29. (with P. Kaplan) |
|
Binomial coefficients and Jacobi sums, Trans. Amer. Math. Soc. 281 (1984), 431-505. (with R. H. Hudson) |
|
An observation on binary quadratic forms of discriminant -32q, Abh. Math. Sem. Univ. Hamburg 53 (1983), 39-40. (with P. A. Leonard) |
|
On the divisibility of the class number of Q(√-pq) by 16, Proc. Edinburgh Math. Soc. 26 (1983), 221-231. (with P. A. Leonard) |
|
On the quadratic residues (mod p) in the interval (0, p/4), Canad. Math. Bull. 26 (1983), 123-124. |
|
On Legendre's equation ax² + by² + cz² = 0, J. Number Theory 16 (1983), 100-105. (with R. H. Hudson) |
|
Extensions of theorems of Cunningham-Aigner and Hasse-Evans, Pacific J. Math. 104 (1983), 111-132. (with R. H. Hudson) |
|
Congruences for representations of primes by binary quadratic forms, Acta Arith. 41 (1982), 311-322. (with R. H. Hudson) |
|
An application of a formula of Western to the evaluation of certain Jacobsthal sums, Acta Arith. 41 (1982), 261-276. (with R. H. Hudson) |
|
Class number formulae of Dirichlet type, Math. Comp. 39 (1982), 725-732. (with R. H. Hudson) |
|
Congruences modulo 16 for the class numbers of the quadratic fields Q(ñp) and Q(ñ2p) for p a prime congruent to 5 modulo 8, Acta Arith. 40 (1982), 375-397. (with P. Kaplan) |
|
Class numbers and biquadratic reciprocity, Canad. J. Math. 34 (1982), 969-988. (with J. D. Currie) |
|
Congruences modulo 8 for the class numbers of Q(√±p), p ≡ 3 (mod 4) a prime, J. Number Theory 15 (1982), 182-198. |
|
A new formulation of the law of octic reciprocity for primes ≡ ±3 (mod 8) and its consequences, Internat. J. Math. Math. Sci. 5 (1982), 565-584. (with R. H. Hudson) |
|
Cauchy-type congruences for binomial coefficients, Proc. Amer. Math. Soc. 85 (1982), 169-174. (with R. H. Hudson) |
|
On the class numbers of Q(√±2p) modulo 16, for p ≡ 1 (mod 8) a prime, Acta Arith. 40 (1982), 289-296. (with P. Kaplan) |
|
On the divisibility of the class numbers of Q(√-p) and Q(√-2p) by 16, Canad. Math. Bull. 25 (1982), 200-206. (with P. A. Leonard) |
|
Resolution of ambiguities in the evaluation of cubic and quartic Jacobsthal sums, Pacific J. Math. 99 (1982), 379-386. (with R. H. Hudson) |
|
An Artin character and representations of primes by binary quadratic forms. II, Manuscripta Math. 37 (1982), 357-381. (with F. Halter-Koch and P. Kaplan) |
|
A divisibility property of binomial coefficients viewed as an elementary sieve, Internat. J. Math. Math. Sci. 4 (1981), 731-743. (with R. H. Hudson) |
|
A new criterion for 7 to be a fourth power (mod p), Israel J. Math. 38 (1981), 221-230. (with R. H. Hudson) |
|
A representation problem involving binary quadratic forms, Arch. Math. (Basel) 36 (1981), 53-56. (with P. A. Leonard) |
|
An Artin character and representation of primes by binary quadratic forms, Manuscripta Math. 33 (1981), 339-356. (with P. Kaplan) |
|
Note on the quadratic character of a quadratic unit, Pacific J. Math. 92 (1981), 35-38. (with D. A. Buell and P. A. Leonard) |
|
The class number of Q(√p) modulo 4, for p ≡ 5 (mod 8) a prime, Pacific J. Math. 92 (1981), 241-248. |
|
The class number of Q(√-2p) modulo 8, for p ≡ 5 (mod 8) a prime, Rocky Mountain J. Math. 11 (1981), 19-26. |
|
On the class number of Q(√-p) modulo 16, for p ≡ 1 (mod 8) a prime, Acta Arith. 39 (1981), 381-398. |
|
Some new residuacity criteria, Pacific J. Math. 91 (1980), 135-143. (with R. H. Hudson) |
|
The quartic character of certain quadratic units, J. Number Theory 12 (1980), 106-109. (with P. A. Leonard) |
|
On the evaluation of (εq1q2/p), Rocky Mountain J. Math. 10 (1980), 559-573. |
|
On the least quadratic non-residue of a prime p ≡ 3 (mod 4), J. Reine Angew. Math. 318 (1980), 106-109. (with R. H. Hudson) |
|
The class number of Q(√-p) modulo 4, for p ≡ 3 (mod 4) a prime, Pacific J. Math. 83 (1979), 565-570. |
|
The quadratic and quartic character of certain quadratic units. II, Rocky Mountain J. Math. 9 (1979), 683-692. (with P. A. Leonard) |
|
An octic reciprocity law of Scholz type, Proc. Amer. Math. Soc. 77 (1979), 315-318. (with D. A. Buell) |
|
Evaluation of character sums connected with elliptic curves, Proc. Amer. Math. Soc. 73 (1979), 291-299. |
|
Remark on an assertion of Chowla, Norske Vid. Selsk. Skr. (Trondheim), No. 1 (1979), 3-4. |
|
Evaluation of certain Jacobsthal sums, Boll. Un. Mat. Ital. 15 (1978), 717-723. (with P. A. Leonard) |
|
Is there an octic reciprocity law of Scholz type?, Amer. Math. Monthly 85 (1978), 483-484. (with D. A. Buell) |
|
Note on Brewer's character sum, Proc. Amer. Math. Soc. 71 (1978), 153-154. |
|
Maximal residue difference sets modulo p, Proc. Amer. Math. Soc. 69 (1978), 205-209. (with D. A. Buell) |
|
On Eisenstein's supplement to the law of cubic reciprocity, Bull. Calcutta Math. Soc. 69 (1977), 311-314. |
|
On the imaginary bicyclic biquadratic fields with class-number 2, Math. Comp. 31 (1977), 1034-1042. (with D. A. Buell and H. C. Williams) |
|
On Scholz's reciprocity law, Proc. Amer. Math. Soc. 64 (1977), 45-46. |
|
Note on Burde's rational biquadratic reciprocity theorem, Canad. Math. Bull. 20 (1977), 145-146. |
|
A rational sixteenth power reciprocity law, Acta Arith. 33 (1977), 365-377. (with P. A. Leonard) |
|
The quadratic and quartic character of certain quadratic units. I, Pacific J. Math. 71 (1977), 101-106. (with P. A. Leonard) |
|
Pedoe's formulation of Urquhart's theorem, Ontario Mathematics Gazette 15 (1976), 42-44. |
|
On the supplement to the law of biquadratic reciprocity, Proc. Amer. Math. Soc. 59 (1976), 19-22. |
|
Explicit criteria for quintic residuacity, Math. Comp. 30 (1976), 847-853. |
|
A rational octic reciprocity law, Pacific J. Math. 63 (1976), 563-570. |
|
Explicit forms of Kummer's complementary theorems to his law of quintic reciprocity, J. Reine Angew. Math. 288 (1976), 207-210. |
|
Note on a result of Barrucand and Cohn, J. Reine Angew. Math. 285 (1976), 218-220. |
|
The eleventh power character of 2, J. Reine Angew. Math. 286/287 (1976), 213-222. (with P. A. Leonard and B. C. Mortimer) |
|
On Urquhart's elementary theorem of Euclidean geometry, Eureka 2 (1976), 108-109. |
|
Cubic nonresidues (mod p), Delta (Waukesha) 6 (1976), 23-28. |
|
Note on a result of Kaplan, Proc. Amer. Math. Soc. 56 (1976), 34-36. |
|
The quadratic character of 2 mod p, Math. Mag. 49 (1976). 89-90. |
|
The cyclotomic numbers of order eleven, Acta Arith. 26 (1975), 365-383. (with P. A. Leonard) |
|
On Euler's criterion for quintic nonresidues, Pacific J. Math. 61 (1975), 543-550. |
|
2 as a ninth power (mod p), J. Indian Math. Soc. 39 (1975), 167-172. |
|
Note on non-Euclidean principal ideal domains, Math. Mag. 48 (1975), 176-177. |
|
On Euler's criterion for cubic nonresidues, Proc. Amer. Math. Soc. 49 (1975), 277-283. |
|
The cyclotomic numbers of order seven, Proc. Amer. Math. Soc. 51 (1975), 295-300. (with P. A. Leonard) |
|
Note on a cubic character sum, Aequationes Math. 12 (1975), 229-231. |
|
Note on integers representable by binary quadratic forms, Canad. Math. Bull. 18 (1975), 123-125. |
|
Note on cubics over GF(2n) and GF(3n), J. Number Theory 7 (1975), 361-365. |
|
Note on the supplement to the law of cubic reciprocity, Proc. Amer. Math. Soc. 47 (1975), 333-334. |
|
Jacobi sums and a theorem of Brewer, Rocky Mountain J. Math. 5 (1975), 301-308. (Erratum 6 (1976), 509.) |
|
The septic character of 2, 3, 5 and 7, Pacific J. Math. 52 (1974), 142-147. (with P. A. Leonard) |
|
3 as a ninth power (mod p), Math. Scand. 35 (1974), 309-317. |
|
Elementary treatment of a quadratic partition of primes p ≡ 1 (mod 7), Illinois J. Math. 18 (1974), 608-621. |
|
A quadratic partition of primes p ≡ 1 (mod 7), Math. Comp. 28 (1974), 1133-1136. |
|
A diophantine system of Dickson, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 56 (1974), 145-150. (with P. A. Leonard) |
|
Forms representable by integral binary quadratic forms, Acta Arith. 26 (1974), 1-9. (with P. A. Leonard) |
|
Note on a paper of S. Uchiyama, Canad. Math. Bull. 17 (1974), 289-293. (with B. C. Mortimer) |
|
On certain sums of fractional parts, Arch. Math. (Basel) 25 (1974), 41-44. (with J. M. Gandhi) |
|
Mertens' theorem for arithmetic progressions, J. Number Theory 6 (1974), 353-359. |
|
The Kloosterman sum revisited, Canad. Math. Bull. 16 (1973), 363-365. |
|
Representability of binary quadratic forms over a Bézout domain, Duke Math. J. 40 (1973), 533-539. (with P. A. Leonard) |
|
Note on extensions of the rationals by square roots, Delta (Waukesha) 3 (1973), 11-15. |
|
Another proof of a theorem of Niven, Math. Mag. 46 (1973), 39. |
|
Quartics over GF(2n), Proc. Amer. Math. Soc. 36 (1972), 347-350. (with P. A. Leonard) |
|
On the number of distinguished representations of a group element, Duke Math. J. 39 (1972), 521-527. (with D. Jacobson) |
|
Products of polynomials over a finite field, Delta (Waukesha) 3 (1972), 35-37. |
|
Exponential sums over GF(2n), Pacific J. Math. 40 (1972), 511-519. |
|
Representation of a binary quadratic form as a sum of two squares, Proc. Amer. Math. Soc. 32 (1972), 368-370. |
|
Forms representable by an integral positive-definite binary quadratic form, Math. Scand. 29 (1971), 73-86. |
|
Small solutions of the congruence a1x1l1 + a2x2l2 + a0 ≡ 0 (mod p), Proc. Cambridge Philos. Soc. 70 (1971), 409-412. |
|
On the solution of linear G.C.D. equations, Pacific J. Math. 39 (1971), 187-206. (with D. Jacobson) |
|
Note on Salié's sum, Proc. Amer. Math. Soc. 30 (1971), 393-394. |
|
On  , Math. Mag. 44 (1971), 273-276. |
|
Note on the number of solutions of f(x1) = f(x2) = ... = f(xr) over a finite field, Canad. Math. Bull. 14 (1971), 429-432. |
|
Note on Dickson's permutation polynomials, Duke Math. J. 38 (1971), 659-665. |
|
Note on the Kloosterman sum, Proc. Amer. Math. Soc. 30 (1971), 61-62. |
|
Note on a theorem of Pall, Proc. Amer. Math. Soc. 28 (1971), 315-316. |
|
On Salié's sum, J. Number Theory 3 (1971), 316-317. |
|
Note on  , Math. Mag. 44 (1971), 9-11. |
|
A distribution property of the solutions of a congruence modulo a large prime, J. Number Theory 3 (1971), 19-32. |
|
A class of character sums, J. London Math. Soc. 3 (1971), 67-72. |
|
Asymptotic behaviour of the nth term of certain subsequences of the natural numbers, Delta (Waukesha) 2 (1970), 1-11. |
|
Integers of biquadratic fields, Canad. Math. Bull. 13 (1970), 519-526. |
|
Finite transformation formulae involving the Legendre symbol, Pacific J. Math. 34 (1970), 559-568. |
|
On a result of Libri and Lebesgue, Amer. Math. Monthly 77 (1970), 610-613. |
|
Small solutions of the congruence ax2 + by2 ≡ c (mod k), Canad. Math. Bull. 12 (1969), 311-320. |
|
Note on factorable polynomials, Canad. Math. Bull. 12 (1969), 589-595. |
|
The distribution of solutions of congruences: Corrigendum and Addendum, Mathematika 16 (1969), 98-100. (with J. H. H. Chalk) |
|
Distinct values of a polynomial in subsets of a finite field, Canad. J. Math. 21 (1969), 1483-1488. |
|
Polynomials with irreducible factors of specified degree, Canad. Math. Bull. 12 (1969), 221-223. |
|
On two conjectures of Chowla, Canad. Math. Bull. 12 (1969), 545-565. |
|
Addendum to "On a theorem of Niven", Canad. Math. Bull. 11 (1968), 145. |
|
Note on pairs of consecutive residues of polynomials, Canad. Math. Bull. 11 (1968), 79-83. |
|
On exceptional polynomials, Canad. Math. Bull. 11 (1968), 279-282. |
|
Quadratic polynomials with the same residues, Amer. Math. Monthly 75 (1968), 969-973. |
|
Cubic polynomials with the same residues (mod p), Proc. Cambridge Philos. Soc. 64 (1968), 655-658 (with K. McCann). |
|
The distribution of the residues of a quartic polynomial, Glasgow Math. J. 8 (1967), 67-88. (with K. McCann) |
|
On extremal polynomials, Canad. Math. Bull. 10 (1967), 585-594. |
|
On general polynomials, Canad. Math. Bull. 10 (1967), 579-583. |
|
Pairs of consecutive residues of polynomials, Canad. J. Math. 19 (1967), 655-666. |
|
A sum of fractional parts, Amer. Math. Monthly 74 (1967), 978-980. |
|
On a theorem of Niven, Canad. Math. Bull. 10 (1967), 573-578. |
|
An elementary number-theoretic formula, Math. Student 35 (1967), 47-50. |
|
On the residues of a cubic polynomial (mod p), Canad. Math. Bull. 10 (1967), 29-38. (with K. McCann) |
|
On the least non-residue of a quartic polynomial, Proc. Cambridge Philos. Soc. 62 (1966), 429-431. |
|
A sum of fractional parts. II., J. Natur. Sci. and Math. 6 (1966), 209-216. |
|
Eisenstein's criteria for absolute irreducibility over a finite field, Canad. Math. Bull. 9 (1966), 575-580. |
|
On the number of solutions of a congruence, Amer. Math. Monthly 73 (1966), 44-49. |
|
The distribution of solutions of congruences, Mathematika 12 (1965), 176-192. (with J. H. H. Chalk) |
|
On Norrie's identity, Math. Mag. 37 (1964), 322. |
|
A note on the quadratic form ax2 + 2bxy + cy2, Math. Gaz. 48 (1964), 290-291. |
|
On the factorization of the first four composite Mersenne numbers, Math. Gaz. 48 (1964), 213. |
|
A simple norm inequality, Amer. Math. Monthly 71 (1964), 53-54. (with C. F. Dunkl) |
|
On the divisibility of F6 by 274, 177, Math. Gaz. 46 (1962), 315-316. |
|
A generalisation of Cardan's solution of the cubic, Math. Gaz. 46 (1962), 221-223. |