Collected Papers of Kenneth S. Williams |
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View Publications by Year: |
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 simplest D4-octics, International Journal of Algebra 2 (2008), 79-89.(with B. K. Spearman) |
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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) |
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Reducibility and the Galois group of a parametric family of quintic polynomials, Missouri J. of Math. Sci. 19 (2007), 2-10. (with M. J. Lavallee and B. K. Spearman) |
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Irreducible quartic polynomials with factorizations modulo p, Amer. Math. Monthly 112 (2005), 876-890. (with E. Driver and P. A. Leonard) |
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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) |
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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) |
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On a procedure for finding the Galois group of a quintic polynomial, Sci. Math. Jpn. 57 (2003), 187-190. (with B. K. Spearman) |
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Uniquely determined unknowns in systems of linear equations, Math. Mag. 75 (2002), 53-57. (with K. Hardy and B. K. Spearman) |
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Commentary on an unpublished lecture by G. N. Watson on solving the quintic, Math.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) |
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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) |
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Note on a paper of Kobayashi and Nakagawa, Sci. Math. Jpn. 53 (2001), 323-334. (with B. K. Spearman) |
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Quartic trinomials with Galois groups A4 and V4, Far East J. Math. Sci. 2 (2000), 665-672. (with B. K. Spearman) |
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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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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. (FJMS) 1 (1999), 137-143. (with B. K. Spearman) |
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The factorization of x5 ± xa + n, Fibonacci Quart. 36 (1998), 158-170. (with 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. |
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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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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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The nth power of a 2 x 2 matrix, Math. Mag. 65 (1992), 336. |
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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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Note on cubics over GF(2n) and GF(3n), J. Number Theory 7 (1975), 361-365. |
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Representability of binary quadratic forms over a Bézout domain, Duke Math. J. 40 (1973), 533-539. (with P. A. Leonard) |
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Note on extensions of the rationals by square roots, Delta (Waukesha) 3 (1973), 11-15. |
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Quartics over GF(2n), Proc. Amer. Math. Soc. 36 (1972), 347-350. (with P. A. Leonard) |
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On the number of distinguished representations of a group element, Duke Math. J. 39 (1972), 521-527. (with D. Jacobson) |
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Products of polynomials over a finite field, Delta (Waukesha) 3 (1972), 35-37. |
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On the solution of linear G.C.D. equations, Pacific J. Math. 39 (1971), 187-206. (with D. Jacobson) |
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Note on Dickson's permutation polynomials, Duke Math. J. 38 (1971), 659-665. |
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Eisenstein's criteria for absolute irreducibility over a finite field, Canad. Math. Bull. 9 (1966), 575-580. |
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A generalisation of Cardan's solution of the cubic, Math. Gaz. 46 (1962), 221-223. |