Lavallee, Melisa J.; Spearman, Blair K.; Williams, Kenneth S. Lifting monogenic cubic fields to monogenic sextic fields. (English) Zbl 1237.11045 Kodai Math. J. 34, No. 3, 410-425 (2011). Reviewer: István Gaál (Debrecen) MSC: 11R04 11R16 11R21 11R32 PDFBibTeX XMLCite \textit{M. J. Lavallee} et al., Kodai Math. J. 34, No. 3, 410--425 (2011; Zbl 1237.11045) Full Text: DOI Link
Spearman, B. K.; Williams, K. S. A normal relative integral basis for the normal closure of a pure cubic field over \(\mathbb Q(\sqrt{-3})\). (English) Zbl 1196.11152 Int. J. Contemp. Math. Sci. 3, No. 29-32, 1427-1432 (2008). Reviewer: István Gaál (Debrecen) MSC: 11R33 11R16 PDFBibTeX XMLCite \textit{B. K. Spearman} and \textit{K. S. Williams}, Int. J. Contemp. Math. Sci. 3, No. 29--32, 1427--1432 (2008; Zbl 1196.11152) Full Text: Link
Spearman, Blair K.; Williams, Kenneth S. The proportion of cyclic quartic field discriminants divisible by a given prime. (English) Zbl 1156.11044 Kobe J. Math. 23, No. 1-2, 1-10 (2006). Reviewer: Abdelmalek Azizi (Oujda) MSC: 11R47 11R16 11R29 PDFBibTeX XMLCite \textit{B. K. Spearman} and \textit{K. S. Williams}, Kobe J. Math. 23, No. 1--2, 1--10 (2006; Zbl 1156.11044)
Spearman, Blair K.; Williams, Kenneth S. The prime ideal factorization of 2 in pure quartic fields with index 2. (English) Zbl 1175.11061 Math. J. Okayama Univ. 48, 43-46 (2006). Reviewer: Abdelmalek Azizi (Oujda) MSC: 11R16 11R27 11R29 PDFBibTeX XMLCite \textit{B. K. Spearman} and \textit{K. S. Williams}, Math. J. Okayama Univ. 48, 43--46 (2006; Zbl 1175.11061)
Alaca, Şaban; Spearman, Blair K.; Williams, Kenneth S. Explicit decomposition of a rational prime in a cubic field. (English) Zbl 1153.11054 Int. J. Math. Math. Sci. 2006, No. 10, 17641, 11 p. (2006). Reviewer: Richard A. Mollin (Calgary) MSC: 11R16 11R09 PDFBibTeX XMLCite \textit{Ş. Alaca} et al., Int. J. Math. Math. Sci. 2006, No. 10, 17641, 11 p. (2006; Zbl 1153.11054) Full Text: DOI EuDML
Silvester, Alan K.; Spearman, Blair K.; Williams, Kenneth S. Cyclic cubic fields of given conductor and given index. (English) Zbl 1104.11047 Can. Math. Bull. 49, No. 3, 472-480 (2006). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11R16 11R29 PDFBibTeX XMLCite \textit{A. K. Silvester} et al., Can. Math. Bull. 49, No. 3, 472--480 (2006; Zbl 1104.11047) Full Text: DOI
Williams, Kenneth S. An extension of Vulakh’s theorem on units in complex cubic fields. (English) Zbl 1095.11051 Far East J. Math. Sci. (FJMS) 14, No. 1, 1-7 (2004). Reviewer: Abdelmalek Azizi (Oujda) MSC: 11R16 11R27 11R09 PDFBibTeX XMLCite \textit{K. S. Williams}, Far East J. Math. Sci. (FJMS) 14, No. 1, 1--7 (2004; Zbl 1095.11051)
Spearman, Blair K.; Williams, Kenneth S. On the Lagrange resolvents of a dihedral quintic polynomial. (English) Zbl 1126.11059 Int. J. Math. Math. Sci. 2004, No. 69-72, 3817-3820 (2004). Reviewer: Olaf Ninnemann (Berlin) MSC: 11R16 11R21 PDFBibTeX XMLCite \textit{B. K. Spearman} and \textit{K. S. Williams}, Int. J. Math. Math. Sci. 2004, No. 69--72, 3817--3820 (2004; Zbl 1126.11059) Full Text: DOI EuDML
Spearman, Blair K.; Williams, Kenneth S. Density of integers which are discriminants of cyclic fields of odd prime degree. (English) Zbl 1056.11068 Arch. Math. 83, No. 6, 507-513 (2004). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11R29 11N25 11R16 11R20 PDFBibTeX XMLCite \textit{B. K. Spearman} and \textit{K. S. Williams}, Arch. Math. 83, No. 6, 507--513 (2004; Zbl 1056.11068) Full Text: DOI
Alaca, Şaban; Williams, Kenneth S. On Voronoi’s method for finding an integral basis of a cubic field. (English) Zbl 1061.11056 Util. Math. 65, 163-166 (2004). Reviewer: Franz Lemmermeyer (Bilkent) MSC: 11R16 11R29 11R04 PDFBibTeX XMLCite \textit{Ş. Alaca} and \textit{K. S. Williams}, Util. Math. 65, 163--166 (2004; Zbl 1061.11056)
Williams, Kenneth S. On real cubic fields with a unique fundamental unit. (English) Zbl 1047.11104 Far East J. Math. Sci. (FJMS) 12, No. 1, 1-7 (2004). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11R16 11R27 12D10 PDFBibTeX XMLCite \textit{K. S. Williams}, Far East J. Math. Sci. (FJMS) 12, No. 1, 1--7 (2004; Zbl 1047.11104)
Alaca, Şaban; Williams, Kenneth S. A simple method for finding an integral basis of a quartic field defined by a trinomial \(x^ 4+ax+b\). (English) Zbl 1056.11057 JP J. Algebra Number Theory Appl. 3, No. 3, 477-505 (2003). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11R16 11R29 PDFBibTeX XMLCite \textit{Ş. Alaca} and \textit{K. S. Williams}, JP J. Algebra Number Theory Appl. 3, No. 3, 477--505 (2003; Zbl 1056.11057)
Spearman, Blair K.; Williams, Kenneth S. Density of integers which are discriminants of cyclic cubic fields. (English) Zbl 1041.11068 Far East J. Math. Sci. (FJMS) 8, No. 1, 83-87 (2003). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11R16 11R29 PDFBibTeX XMLCite \textit{B. K. Spearman} and \textit{K. S. Williams}, Far East J. Math. Sci. (FJMS) 8, No. 1, 83--87 (2003; Zbl 1041.11068)
Silvester, Alan K.; Spearman, Blair K.; Williams, Kenneth S. The index of a dihedral quartic field. (English) Zbl 1049.11115 JP J. Algebra Number Theory Appl. 3, No. 1, 121-144 (2003). Reviewer: Michael Pohst (Berlin) MSC: 11R16 PDFBibTeX XMLCite \textit{A. K. Silvester} et al., JP J. Algebra Number Theory Appl. 3, No. 1, 121--144 (2003; Zbl 1049.11115)
Spearman, Blair K.; Williams, Kenneth S. The index of a cyclic quartic field. (English) Zbl 1049.11111 Monatsh. Math. 140, No. 1, 19-70 (2003). Reviewer: Istvan Gaál (Debrecen) MSC: 11R04 11R16 11R29 PDFBibTeX XMLCite \textit{B. K. Spearman} and \textit{K. S. Williams}, Monatsh. Math. 140, No. 1, 19--70 (2003; Zbl 1049.11111) Full Text: DOI
Spearman, Blair K.; Williams, Kenneth S. Integers which are discriminants of bicyclic or cyclic quartic fields. (English) Zbl 1038.11068 JP J. Algebra Number Theory Appl. 1, No. 3, 179-194 (2001). Reviewer: Hideo Yokoi (Aichi) MSC: 11R16 11R29 PDFBibTeX XMLCite \textit{B. K. Spearman} and \textit{K. S. Williams}, JP J. Algebra Number Theory Appl. 1, No. 3, 179--194 (2001; Zbl 1038.11068)
Ou, Zhiming M.; Williams, Kenneth S. On the density of cyclic quartic fields. (English) Zbl 0996.11068 Can. Math. Bull. 44, No. 1, 97-104 (2001). Reviewer: Hideo Yokoi (Aichi) MSC: 11R16 11R29 PDFBibTeX XMLCite \textit{Z. M. Ou} and \textit{K. S. Williams}, Can. Math. Bull. 44, No. 1, 97--104 (2001; Zbl 0996.11068) Full Text: DOI
Spearman, B. K.; Williams, K. S. Relative integral bases for quartic fields over quadratic subfields. (English) Zbl 0853.11090 Acta Math. Hung. 70, No. 3, 185-192 (1996). Reviewer: C.Parry (Blacksburg) MSC: 11R29 11R16 11R11 PDFBibTeX XMLCite \textit{B. K. Spearman} and \textit{K. S. Williams}, Acta Math. Hung. 70, No. 3, 185--192 (1996; Zbl 0853.11090) Full Text: DOI
Spearman, Blair K.; Williams, Kenneth S. Unramified quadratic extensions of a quadratic field. (English) Zbl 0842.11037 Rocky Mt. J. Math. 25, No. 2, 783-788 (1995). Reviewer: F.Halter-Koch (Graz) MSC: 11R16 11S15 PDFBibTeX XMLCite \textit{B. K. Spearman} and \textit{K. S. Williams}, Rocky Mt. J. Math. 25, No. 2, 783--788 (1995; Zbl 0842.11037) Full Text: DOI
Huard, James G.; Spearman, Blair K.; Williams, Kenneth S. Integral bases for quartic fields with quadratic subfields. (English) Zbl 0826.11048 J. Number Theory 51, No. 1, 87-102 (1995). Reviewer: H.Yokoi (Nagoya) MSC: 11R16 11R11 PDFBibTeX XMLCite \textit{J. G. Huard} et al., J. Number Theory 51, No. 1, 87--102 (1995; Zbl 0826.11048) Full Text: DOI
Hardy, Kenneth; Hudson, Richard H.; Richman, David; Williams, Kenneth S. Determination of all imaginary cyclic quartic fields with class number 2. (English) Zbl 0678.12003 Trans. Am. Math. Soc. 311, No. 1, 1-55 (1989). Reviewer: C.Parry MSC: 11R16 11R23 11R18 PDFBibTeX XMLCite \textit{K. Hardy} et al., Trans. Am. Math. Soc. 311, No. 1, 1--55 (1989; Zbl 0678.12003) Full Text: DOI
Hardy, Kenneth; Hudson, R. H.; Richman, D.; Williams, Kenneth S.; Holtz, N. M. Calculation of the class numbers of imaginary cyclic quartic fields. (English) Zbl 0624.12004 Math. Comput. 49, 615-620 (1987). MSC: 11R21 11R23 12-04 PDFBibTeX XMLCite \textit{K. Hardy} et al., Math. Comput. 49, 615--620 (1987; Zbl 0624.12004) Full Text: DOI
Williams, Kenneth S. The class number two problem for certain quartic fields. (English) Zbl 0617.12007 Algebraic number theory, Proc. Symp. RIMS, Kyoto/Jap. 1986, RIMS Kokyuroku 603, 51-59 (1987). MSC: 11R21 11R23 PDFBibTeX XML
Williams, Kenneth S. The class number two problem for certain quartic fields. (English) Zbl 0615.12011 Numerical mathematics and computing, Proc. 16th Conf., Winnipeg/Manit. 1986, Congr. Numerantium 56, 63-70 (1987). Reviewer: R.Mollin MSC: 11R23 11R16 12-04 PDFBibTeX XML
Williams, Kenneth S. Calculation of the class numbers of certain quartic fields. (English) Zbl 0615.12008 Class numbers and fundamental units of algebraic number fields, Proc. Int. Conf., Katata/Jap. 1986, 139-150 (1986). MSC: 11R23 12-04 11R16 PDFBibTeX XML
Williams, Kenneth S.; Friesen, Christian; Howe, Lawrence J. Criteria for biquadratic residuacity modulo a prime \(p\) involving quaternary representations of \(p\). (English) Zbl 0573.10003 Can. J. Math. 37, 337-370 (1985). Reviewer: A. R. Rajwade (Chandigarh) MSC: 11A15 11E20 11R18 11T22 11R29 PDFBibTeX XMLCite \textit{K. S. Williams} et al., Can. J. Math. 37, 337--370 (1985; Zbl 0573.10003) Full Text: DOI
Buell, Duncan A.; Hudson, Richard H.; Williams, Kenneth S. Extension of a theorem of Cauchy and Jacobi. (English) Zbl 0551.12014 J. Number Theory 19, 309-340 (1984). Reviewer: A.R.Rajwade MSC: 11T55 11A15 11E20 11T22 PDFBibTeX XMLCite \textit{D. A. Buell} et al., J. Number Theory 19, 309--340 (1984; Zbl 0551.12014) Full Text: DOI