Collected Papers of Kenneth S. Williams

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Algebraic Number Theory - Analytic Number Theory - Elementary Number Theory - Computational Number Theory - Analysis - Algebra - Geometry - Linear Algebra - Other

ANNT The class number of Q(√-p) modulo 4, for p ≡ 3 (mod 4) a prime, Pacific J. Math. 83 (1979), 565-570.
ALNT The quadratic and quartic character of certain quadratic units. II, Rocky Mountain J. Math. 9 (1979), 683-692. (with P. A. Leonard)
ALNT An octic reciprocity law of Scholz type, Proc. Amer. Math. Soc. 77 (1979), 315-318. (with D. A. Buell)
ALNT Evaluation of character sums connected with elliptic curves, Proc. Amer. Math. Soc. 73 (1979), 291-299.
ALNT Remark on an assertion of Chowla, Norske Vid. Selsk. Skr. (Trondheim), No. 1 (1979), 3-4.
ALNT Evaluation of certain Jacobsthal sums, Boll. Un. Mat. Ital. 15 (1978), 717-723. (with P. A. Leonard)
ALNT Is there an octic reciprocity law of Scholz type?, Amer. Math. Monthly 85 (1978), 483-484. (with D. A. Buell)
ALNT, ENT Note on Brewer's character sum, Proc. Amer. Math. Soc. 71 (1978), 153-154.
ANNT Maximal residue difference sets modulo p, Proc. Amer. Math. Soc. 69 (1978), 205-209. (with D. A. Buell)
ALNT On Eisenstein's supplement to the law of cubic reciprocity, Bull. Calcutta Math. Soc. 69 (1977), 311-314.
ALNT, CNT On the imaginary bicyclic biquadratic fields with class-number 2, Math. Comp. 31 (1977), 1034-1042. (with D. A. Buell and H. C. Williams)
ALNT On Scholz's reciprocity law, Proc. Amer. Math. Soc. 64 (1977), 45-46.
ALNT Note on Burde's rational biquadratic reciprocity theorem, Canad. Math. Bull. 20 (1977), 145-146.
ALNT A rational sixteenth power reciprocity law, Acta Arith. 33 (1977), 365-377. (with P. A. Leonard)
ALNT The quadratic and quartic character of certain quadratic units. I, Pacific J. Math. 71 (1977), 101-106. (with P. A. Leonard)
GEOM Pedoe's formulation of Urquhart's theorem, Ontario Mathematics Gazette 15 (1976), 42-44.
ALNT On the supplement to the law of biquadratic reciprocity, Proc. Amer. Math. Soc. 59 (1976), 19-22.
ALNT Explicit criteria for quintic residuacity, Math. Comp. 30 (1976), 847-853.
ALNT A rational octic reciprocity law, Pacific J. Math. 63 (1976), 563-570.
ALNT Explicit forms of Kummer's complementary theorems to his law of quintic reciprocity, J. Reine Angew. Math. 288 (1976), 207-210.
ALNT Note on a result of Barrucand and Cohn, J. Reine Angew. Math. 285 (1976), 218-220.
ALNT The eleventh power character of 2, J. Reine Angew. Math. 286/287 (1976), 213-222. (with P. A. Leonard and B. C. Mortimer)
GEOM On Urquhart's elementary theorem of Euclidean geometry, Eureka 2 (1976), 108-109.
ALNT Cubic nonresidues (mod p), Delta (Waukesha) 6 (1976), 23-28.
ALNT Note on a result of Kaplan, Proc. Amer. Math. Soc. 56 (1976), 34-36.
ENT The quadratic character of 2 mod p, Math. Mag. 49 (1976). 89-90.
ALNT The cyclotomic numbers of order eleven, Acta Arith. 26 (1975), 365-383. (with P. A. Leonard)
ALNT On Euler's criterion for quintic nonresidues, Pacific J. Math. 61 (1975), 543-550.
ALNT 2 as a ninth power (mod p), J. Indian Math. Soc. 39 (1975), 167-172.
ALNT Note on non-Euclidean principal ideal domains, Math. Mag. 48 (1975), 176-177.
ALNT On Euler's criterion for cubic nonresidues, Proc. Amer. Math. Soc. 49 (1975), 277-283.
ALNT The cyclotomic numbers of order seven, Proc. Amer. Math. Soc. 51 (1975), 295-300. (with P. A. Leonard)
ALNT Note on a cubic character sum, Aequationes Math. 12 (1975), 229-231.
ANNT Note on integers representable by binary quadratic forms, Canad. Math. Bull. 18 (1975), 123-125.
Algebra Note on cubics over GF(2n) and GF(3n), J. Number Theory 7 (1975), 361-365.
ALNT Note on the supplement to the law of cubic reciprocity, Proc. Amer. Math. Soc. 47 (1975), 333-334.
ALNT Jacobi sums and a theorem of Brewer, Rocky Mountain J. Math. 5 (1975), 301-308. (Erratum 6 (1976), 509.)
ALNT The septic character of 2, 3, 5 and 7, Pacific J. Math. 52 (1974), 142-147. (with P. A. Leonard)
ALNT 3 as a ninth power (mod p), Math. Scand. 35 (1974), 309-317.
ENT Elementary treatment of a quadratic partition of primes p ≡ 1 (mod 7), Illinois J. Math. 18 (1974), 608-621.
CNT A quadratic partition of primes p ≡ 1 (mod 7), Math. Comp. 28 (1974), 1133-1136.
ALNT A diophantine system of Dickson, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 56 (1974), 145-150. (with P. A. Leonard)
ALNT, ENT Forms representable by integral binary quadratic forms, Acta Arith. 26 (1974), 1-9. (with P. A. Leonard)
ALNT, CNT Note on a paper of S. Uchiyama, Canad. Math. Bull. 17 (1974), 289-293. (with B. C. Mortimer)
ENT On certain sums of fractional parts, Arch. Math. (Basel) 25 (1974), 41-44. (with J. M. Gandhi)
ANNT Mertens' theorem for arithmetic progressions, J. Number Theory 6 (1974), 353-359.
ANNT The Kloosterman sum revisited, Canad. Math. Bull. 16 (1973), 363-365.
Algebra Representability of binary quadratic forms over a Bézout domain, Duke Math. J. 40 (1973), 533-539. (with P. A. Leonard)
Algebra Note on extensions of the rationals by square roots, Delta (Waukesha) 3 (1973), 11-15.
ALNT, ENT Another proof of a theorem of Niven, Math. Mag. 46 (1973), 39.
Algebra Quartics over GF(2n), Proc. Amer. Math. Soc. 36 (1972), 347-350. (with P. A. Leonard)
Algebra On the number of distinguished representations of a group element, Duke Math. J. 39 (1972), 521-527. (with D. Jacobson)
Algebra Products of polynomials over a finite field, Delta (Waukesha) 3 (1972), 35-37.
ANNT Exponential sums over GF(2n), Pacific J. Math. 40 (1972), 511-519.
ENT, ALNT Representation of a binary quadratic form as a sum of two squares, Proc. Amer. Math. Soc. 32 (1972), 368-370.
ENT, ALNT Forms representable by an integral positive-definite binary quadratic form, Math. Scand. 29 (1971), 73-86.
ANNT Small solutions of the congruence a1x1l1 + a2x2l2 + a0 ≡ 0 (mod p), Proc. Cambridge Philos. Soc. 70 (1971), 409-412.
Algebra On the solution of linear G.C.D. equations, Pacific J. Math. 39 (1971), 187-206. (with D. Jacobson)
ANNT Note on Salié's sum, Proc. Amer. Math. Soc. 30 (1971), 393-394.
Analysis On , Math. Mag. 44 (1971), 273-276.
ANNT Note on the number of solutions of f(x1) = f(x2) = ... = f(xr) over a finite field, Canad. Math. Bull. 14 (1971), 429-432.
ALNT, Algebra Note on Dickson's permutation polynomials, Duke Math. J. 38 (1971), 659-665.
ANNT Note on the Kloosterman sum, Proc. Amer. Math. Soc. 30 (1971), 61-62.
ALNT, ENT Note on a theorem of Pall, Proc. Amer. Math. Soc. 28 (1971), 315-316.
ANNT On Salié's sum, J. Number Theory 3 (1971), 316-317.
Analysis Note on , Math. Mag. 44 (1971), 9-11.
ANNT A distribution property of the solutions of a congruence modulo a large prime, J. Number Theory 3 (1971), 19-32.
ANNT A class of character sums, J. London Math. Soc. 3 (1971), 67-72.
ANNT Asymptotic behaviour of the nth term of certain subsequences of the natural numbers, Delta (Waukesha) 2 (1970), 1-11.
ALNT Integers of biquadratic fields, Canad. Math. Bull. 13 (1970), 519-526.
ENT, ANNT Finite transformation formulae involving the Legendre symbol, Pacific J. Math. 34 (1970), 559-568.
ENT On a result of Libri and Lebesgue, Amer. Math. Monthly 77 (1970), 610-613.