Collected Papers of Kenneth S. Williams |
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View Publications by Subject: Algebraic Number Theory - Analytic Number Theory - Elementary Number Theory - Computational Number Theory - Analysis - Algebra - Geometry - Linear Algebra - Other |
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 and related series, Mathematical Analysis and Applications (Editor Th. M. Rassias), Hadronic Press, Inc., Florida, 1999, pp. 183-196. (with Zhang Nan-Yue) |
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Dihedral quintic polynomials and a theorem of Galois, Indian J. Pure Appl. Math. 30 (1999), 839-845. (with B. K. Spearman) |
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Some Lambert series expansions of products of theta functions, Ramanujan J. 3 (1999), 367-384. |
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On a formula of Howard, Bull. Hong Kong Math. Soc. 2 (1999), 325-340. (with B. K. Spearman) |
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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) |
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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) |
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DeMoivre's quintic and a theorem of Galois, Far East J. Math. Sci. 1 (1999), 137-143. (with B. K. Spearman) |
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Cyclic quartic fields and F20 quintics, Far East J. Math. Sci. 1 (1999), 121-126. (with B. K. Spearman) |
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Values of the Dedekind eta function at quadratic irrationalities, Canad. J. Math. 51 (1999), 176-224. (with A. J. van der Poorten) |
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The factorization of x5 ± xa + n, Fibonacci Quart. 36 (1998), 158-170. (with B. K. Spearman) |
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Sarvadaman Chowla (1907-1995), Notices Amer. Math. Soc. 45 (1998), 594-598. (with R. G. Ayoub and J. G. Huard) |
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Pascal's triangle (mod 8), European J. Combin. 19 (1998), 45-62. (with J. G. Huard and B. K. Spearman) |
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An explicit integral basis for a pure cubic field, Far East J. Math. Sci. 6 (1998), 1-14. (with B. K. Spearman) |
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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) |
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The conductor of a cyclic quartic field using Gauss sums, Czechoslovak Math. J. 47 (1997), 453-462. (with B. K. Spearman) |
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On Pascal's triangle modulo p2, Colloq. Math. 74 (1997), 157-165. (with J. G. Huard and B. K. Spearman) |
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Pascal's triangle (mod 9), Acta Arith. 78 (1997), 331-349. (with J. G. Huard and B. K. Spearman) |
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On a formula of Dirichlet, Far East J. Math. Sci. 5 (1997), 153-157. (with P. Kaplan) |
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Bernoulli's identity without calculus, Math. Mag. 70 (1997), 47-50. |
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Normal relative integral bases for quartic fields over quadratic subfields, Kodai Math. J. 19 (1996), 293-307. (with B. K. Spearman) |
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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) |
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The intersection of two cyclotomic extensions of a quadratic field, Kyungpook Math. J. 36 (1996), 117-124. (with B. K. Spearman) |
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On solvable quintics X5 + aX + b and X5 + aX2 + b, Rocky Mountain J. Math. 26 (1996), 753-772. (with B. K. Spearman) |
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Relative integral bases for quartic fields over quadratic subfields, Acta Math. Hungar. 70 (1996), 185-192. (with B. K. Spearman) |
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On Tornheim's double series, Acta Arith. 75 (1996), 105-117. (with J. G. Huard and Zhang Nan-Yue) |
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The conductor of a cyclic quartic field, Publ. Math. Debrecen 48 (1996), 13-43. (with B. K. Spearman) |
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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. |
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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) |
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The Chowla-Selberg formula for genera, Acta Arith. 73 (1995), 271-301. (with J. G. Huard and P. Kaplan) |
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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) |
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On the Epstein zeta function, Tamkang J. Math. 26 (1995), 165-176. (with Zhang Nan-Yue) |
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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) |
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Unramified quadratic extensions of a quadratic field, Rocky Mountain J. Math. 25 (1995), 783-788. (with B. K. Spearman) |
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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) |
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Integral bases for quartic fields with quadratic subfields, J. Number Theory 51 (1995), 87-102. (with J. G. Huard and B. K. Spearman) |
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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) |
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The recurrence relation an = (An+B)an-1 + (Cn+D)an-2, Crux. Math. 20 (1994), 91-96. |
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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) |
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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) |
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The primes for which an abelian cubic splits, Tokyo J. Math. 17 (1994), 467-478. (with J. G. Huard and B. K. Spearman) |
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Evaluation of two trigonometric sums, Mathematica Slovaca 44 (1994), 575-583. (with Zhang Nan-Yue) |
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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) |
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Some results on the generalized Stieltjes constants, Analysis 14 (1994), 147-162. (with Zhang Nan-Yue) |
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On finding the solutions of n=au2+buv+cv2 in integers u and v, Utilitas Math. 46 (1994), 3-19. |
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Characterization of solvable quintics x5 + ax + b, Amer. Math. Monthly 101 (1994), 986-992. (with B. K. Spearman) |
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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) |
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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) |
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A refinement of H.C. Williams' qth root algorithm, Math. Comp. 61 (1993), 475-483. (with K. Hardy) |
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Representation of primes in arithmetic progression by binary quadratic forms, J. Number Theory 45 (1993), 61-67. (with P. Kaplan) |
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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) |
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Application of the Hurwitz zeta function to the evaluation of certain integrals, Canad. Math. Bull. 36 (1993), 373-384. (with Zhang Nan-Yue) |
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Some series representations of zeta(2n+1), Rocky Mountain J. Math. 23 (1993), 1581-1592. (with Zhang Nan-Yue) |
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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) |
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The squareroot of an ambiguous form in the principal genus, Proc. Edinburgh Math. Soc. 36 (1992), 145-150. (with K. Hardy) |
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The nth power of a 2 x 2 matrix, Math. Mag. 65 (1992), 336. |
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Mathematical modelling of atom loss in delivery tubing, Canad. J. Chemistry 70 (1992), 1978-1984. (with R. S. Daniels and D. C. Wigfield) |
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An upper bound for the sum for a certain class of functions ƒ, Proc. Amer. Math. Soc. 114 (1992), 29-35. (with E. Dobrowolski) |
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Representing primes by binary quadratic forms, Amer. Math. Monthly 99 (1992), 423-426. (with B. K. Spearman) |
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Determination of modulo p, Acta Arithmetica 61 (1992), 161-172. (with K. Hardy) |
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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) |
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On Yamamoto's reciprocity law, Proc. Amer. Math. Soc. 111 (1991), 607-609. |
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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) |
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On an assertion of Ramanujan concerning binary quadratic forms, J. Number Theory 38 (1991), 118-133. |
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The distance between ideals in the orders of a real quadratic field, Enseign. Math. 36 (1990), 321-358. (with P. Kaplan) |
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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) |
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On Eisenstein's problem, Acta Arithmetica 54 (1990), 323-345. (with N. Ishii and P. Kaplan) |
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Solving n = au2+buv+cv2 using the Euclidean algorithm, Utilitas Math. 38 (1990), 225-236. (with K. Hardy and J. B. Muskat) |
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Evaluation of the infinite series , Proc. Amer. Math. Soc. 109 (1990), 597-603. (with K. Hardy) |
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The integers of a cyclic quartic field, Rocky Mountain J. Math. 20 (1990), 145-150. (with R. H. Hudson) |