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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The class number of pairs of positive-definite binary quadratic forms, Acta Aritmetica 52 (1989), 103-117. (with K. Hardy) |
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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) |
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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) |
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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) |
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On the size of a solution of Legendre's equation, Utilitas Math. 34 (1988), 65-72. |
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Cyclic quartic fields with relative integral bases over their quadratic subfields, Proc. Amer. Math. Soc. 103 (1988), 687-694. (with B. K. Spearman) |
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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. |
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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) |
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The cyclotomic numbers of order fifteen, Math. Comp. 48 (1987), 67-83. (with N. Buck, L. Smith, and B. K. Spearman) |
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Congruences modulo 16 for the class numbers of complex quadratic fields, J. Number Theory 27 (1987), 178-195. (with K. Hardy) |
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Cyclotomy of order twelve over GF(p²), p² ≡ 1 (mod 12), Math. Comp. 48 (1987), 444-446. (with J. B. Muskat) |
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A congruence relating the class numbers of complex quadratic fields, Acta Arith. 47 (1986), 263-276. (with K. Hardy) |
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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) |
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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) |
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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. |
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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. |
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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) |
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On the solvability of the diophantine equation dV2 - 2eVW - dW2 = 1, Pacific J. Math. 124 (1986), 145-158. (with K. Hardy) |
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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) |
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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) |
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Pell's equations x² - my² = -1, -4 and continued fractions, J. Number Theory 23 (1986), 169-182. (with P. Kaplan) |
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A congruence for the index of a unit of a real abelian number field, Acta. Arith. 46 (1985), 57-72. (with K. Hardy) |
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On the evaluation of the Legendre symbol (A + B√m⁄p), Acta Arith. 45 (1985), 255-272. (with K. Hardy and C. Friesen) |
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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) |
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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) |
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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) |
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Extension of a theorem of Cauchy and Jacobi, J. Number Theory 19 (1984), 309-340. (with D. A. Buell and R. H. Hudson) |
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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) |
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Binomial coefficients and Jacobi sums, Trans. Amer. Math. Soc. 281 (1984), 431-505. (with R. H. Hudson) |
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An observation on binary quadratic forms of discriminant -32q, Abh. Math. Sem. Univ. Hamburg 53 (1983), 39-40. (with P. A. Leonard) |
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On the divisibility of the class number of Q(√-pq) by 16, Proc. Edinburgh Math. Soc. 26 (1983), 221-231. (with P. A. Leonard) |
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On the quadratic residues (mod p) in the interval (0, p/4), Canad. Math. Bull. 26 (1983), 123-124. |
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On Legendre's equation ax² + by² + cz² = 0, J. Number Theory 16 (1983), 100-105. (with R. H. Hudson) |
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Extensions of theorems of Cunningham-Aigner and Hasse-Evans, Pacific J. Math. 104 (1983), 111-132. (with R. H. Hudson) |
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Congruences for representations of primes by binary quadratic forms, Acta Arith. 41 (1982), 311-322. (with R. H. Hudson) |
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An application of a formula of Western to the evaluation of certain Jacobsthal sums, Acta Arith. 41 (1982), 261-276. (with R. H. Hudson) |
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Class number formulae of Dirichlet type, Math. Comp. 39 (1982), 725-732. (with R. H. Hudson) |
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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) |
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Class numbers and biquadratic reciprocity, Canad. J. Math. 34 (1982), 969-988. (with J. D. Currie) |
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Congruences modulo 8 for the class numbers of Q(√±p), p ≡ 3 (mod 4) a prime, J. Number Theory 15 (1982), 182-198. |
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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) |
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Cauchy-type congruences for binomial coefficients, Proc. Amer. Math. Soc. 85 (1982), 169-174. (with R. H. Hudson) |
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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) |
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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) |
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Resolution of ambiguities in the evaluation of cubic and quartic Jacobsthal sums, Pacific J. Math. 99 (1982), 379-386. (with R. H. Hudson) |
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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) |
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A divisibility property of binomial coefficients viewed as an elementary sieve, Internat. J. Math. Math. Sci. 4 (1981), 731-743. (with R. H. Hudson) |
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A new criterion for 7 to be a fourth power (mod p), Israel J. Math. 38 (1981), 221-230. (with R. H. Hudson) |
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A representation problem involving binary quadratic forms, Arch. Math. (Basel) 36 (1981), 53-56. (with P. A. Leonard) |
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An Artin character and representation of primes by binary quadratic forms, Manuscripta Math. 33 (1981), 339-356. (with P. Kaplan) |
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Note on the quadratic character of a quadratic unit, Pacific J. Math. 92 (1981), 35-38. (with D. A. Buell and P. A. Leonard) |
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The class number of Q(√p) modulo 4, for p ≡ 5 (mod 8) a prime, Pacific J. Math. 92 (1981), 241-248. |
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The class number of Q(√-2p) modulo 8, for p ≡ 5 (mod 8) a prime, Rocky Mountain J. Math. 11 (1981), 19-26. |
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On the class number of Q(√-p) modulo 16, for p ≡ 1 (mod 8) a prime, Acta Arith. 39 (1981), 381-398. |
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Some new residuacity criteria, Pacific J. Math. 91 (1980), 135-143. (with R. H. Hudson) |
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The quartic character of certain quadratic units, J. Number Theory 12 (1980), 106-109. (with P. A. Leonard) |
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On the evaluation of (εq1q2/p), Rocky Mountain J. Math. 10 (1980), 559-573. |
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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) |