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Williams, Kenneth S.

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Author ID: williams.kenneth-s Recent zbMATH articles by "Williams, Kenneth S."
Published as: Williams, Kenneth S.; Williams, K. S.; Williams, kenneth S.; Wiliams, Kenneth S.
Homepage: http://people.math.carleton.ca/~williams/index.html
External Links: MGP · dblp · GND
Documents Indexed: 378 Publications since 1964, including 11 Books
2 Contributions as Editor
Reviewing Activity: 95 Reviews
Co-Authors: 57 Co-Authors with 268 Joint Publications
553 Co-Co-Authors
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Serials

33 Acta Arithmetica
27 Canadian Mathematical Bulletin
24 Proceedings of the American Mathematical Society
21 Far East Journal of Mathematical Sciences
16 Journal of Number Theory
15 American Mathematical Monthly
15 Pacific Journal of Mathematics
15 International Journal of Number Theory
14 Rocky Mountain Journal of Mathematics
11 Mathematics Magazine
8 Mathematics of Computation
7 Canadian Journal of Mathematics
7 International Journal of Mathematics and Mathematical Sciences
7 JP Journal of Algebra, Number Theory and Applications
6 Journal of Combinatorics and Number Theory
5 Archiv der Mathematik
5 Integers
4 Indian Journal of Pure & Applied Mathematics
4 Journal für die Reine und Angewandte Mathematik
4 Utilitas Mathematica
4 The Ramanujan Journal
3 Bulletin of the Australian Mathematical Society
3 Duke Mathematical Journal
3 Journal of the London Mathematical Society. Second Series
3 Kodai Mathematical Journal
3 Mathematical Journal of Okayama University
3 Proceedings of the Edinburgh Mathematical Society. Series II
3 Proceedings of the Cambridge Philosophical Society
3 Carleton-Ottawa Mathematical Lecture Note Series
3 International Mathematical Forum
3
2 Czechoslovak Mathematical Journal
2 The Fibonacci Quarterly
2 Functiones et Approximatio. Commentarii Mathematici
2 Manuscripta Mathematica
2 Mathematica Scandinavica
2 Mathematika
2 Monatshefte für Mathematik
2 Osaka Journal of Mathematics
2 Tamkang Journal of Mathematics
2 Transactions of the American Mathematical Society
2 L’Enseignement Mathématique. 2e Série
2 Journal de Théorie des Nombres de Bordeaux
2 Far East Journal of Mathematical Sciences
2 Analysis (München)
2 Scientiae Mathematicae Japonicae
2 Missouri Journal of Mathematical Sciences
2 International Journal of Modern Mathematics
1 Communications in Algebra
1 Israel Journal of Mathematics
1 Journal of Mathematical Analysis and Applications
1 The Mathematical Gazette
1 Mathematical Proceedings of the Cambridge Philosophical Society
1 Arkiv för Matematik
1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
1 Bulletin of the Calcutta Mathematical Society
1 Colloquium Mathematicum
1 Dissertationes Mathematicae
1 Glasgow Mathematical Journal
1 Illinois Journal of Mathematics
1 The Journal of the Indian Mathematical Society. New Series
1 Journal of Natural Sciences and Mathematics
1 Kyungpook Mathematical Journal
1 Mathematica Slovaca
1 The Mathematics Student
1 Proceedings of the Japan Academy. Series A
1 Publicationes Mathematicae
1 Tokyo Journal of Mathematics
1 Yokohama Mathematical Journal
1 European Journal of Combinatorics
1 Analysis
1 Acta Mathematica Hungarica
1 Kobe Journal of Mathematics
1 Aequationes Mathematicae
1 Atti della Accademia Nazionale dei Lincei. Serie Ottava. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali
1 Notices of the American Mathematical Society
1 New Zealand Journal of Mathematics
1 Georgian Mathematical Journal
1 Skrifter. Det Kongelige Norske Videnskabers Selskab
1 Taiwanese Journal of Mathematics
1 The Asian Journal of Mathematics
1 The Bulletin of the Hong Kong Mathematical Society
1 Bollettino della Unione Matematica Italiana. Series V. B
1 CRM Proceedings & Lecture Notes
1 Fields Institute Communications
1 London Mathematical Society Student Texts
1 Mathematics and its Applications (Dordrecht)
1 Canadian Mathematical Society Series of Monographs and Advanced Texts
1 International Journal of Contemporary Mathematical Sciences
1 International Journal of Algebra
1 Advances in Theoretical and Applied Mathematics
1 The College Mathematics Journal

Publications by Year

Citations contained in zbMATH Open

249 Publications have been cited 1,645 times in 997 Documents Cited by Year
Gauss and Jacobi sums. Zbl 0906.11001
Berndt, Bruce C.; Evans, Ronald J.; Williams, Kenneth S.
274
1998
Elementary evaluation of certain convolution sums involving divisor functions. Zbl 1062.11005
Huard, James G.; Ou, Zhiming M.; Spearman, Blair K.; Williams, Kenneth S.
47
2002
A simple norm inequality. Zbl 0178.16202
Dunkl, Charles F.; Williams, K. S.
45
1964
Number theory in the spirit of Liouville. Zbl 1227.11002
Williams, Kenneth S.
42
2011
Introductory algebraic number theory. Zbl 1035.11001
Alaca, Şaban; Williams, Kenneth S.
39
2004
Evaluation of the convolution sums \(\sum _{l+6m=n}\sigma (l)\sigma (m)\) and \(\sum _{2l+3m=n}\sigma (l)\sigma (m)\). Zbl 1169.11002
Alaca, Şaban; Williams, Kenneth S.
35
2007
Integers of biquadratic fields. Zbl 0205.35401
Williams, Kenneth S.
30
1970
The convolution sum \(\sum_{m<n/8} \sigma(m) \sigma(n-8m)\). Zbl 1130.11006
Williams, Kenneth S.
30
2006
Nineteen quaternary quadratic forms. Zbl 1131.11025
Alaca, Ayşe; Alaca, Şaban; Lemire, Mathieu F.; Williams, Kenneth S.
30
2007
Note on cubics over \(GF(2^n)\) and \(GF(3^n)\). Zbl 0321.12029
Williams, Kenneth S.
28
1975
The convolution sum \(\sum_{m<n/16}\sigma(m)\sigma(n-16m)\). Zbl 1132.11305
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
26
2008
Evaluation of the convolution sums \(\sum_{l+18m=n}\sigma(l)\sigma(m)\) and \(\sum_{2l+9m=n}\sigma(l)\sigma(m)\). Zbl 1163.11003
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
26
2007
The number of representations of a positive integer by certain octonary quadratic forms. Zbl 1213.11087
Alaca, Şaban; Williams, Kenneth S.
25
2010
The convolution sum \(\sum_{m<n/9}\sigma(m)\sigma(n-9m)\). Zbl 1082.11003
Williams, Kenneth S.
25
2005
Evaluation of the convolution sums \(\sum_{l+12m=n}\sigma(l)\sigma(m)\) and \(\sum_{3l+4m=n}\sigma(l)\sigma(m)\). Zbl 1154.11003
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
24
2006
On the two-dimensional theta functions of the Borweins. Zbl 1127.11035
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
23
2006
Some results on the generalized Stieltjes constants. Zbl 0808.11054
Zhang, Nanyue; Williams, Kenneth S.
21
1994
On Tornheim’s double series. Zbl 0858.40008
Huard, James G.; Williams, Kenneth S.; Zhang, Nanyue
21
1996
Evaluation of the convolution sums \(\sum_{l+24m=n}\sigma(l)\sigma(m)\) and \(\sum_{3l+8m=n}\sigma(l)\sigma(m)\). Zbl 1132.11304
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
19
2007
Integral bases for quartic fields with quadratic subfields. Zbl 0826.11048
Huard, James G.; Spearman, Blair K.; Williams, Kenneth S.
18
1995
Theta functions identities and representations by certain quaternary quadratic forms. Zbl 1163.11029
Alaca, Ayşe; Alaca, Şaban; Lemire, Mathieu F.; Williams, Kenneth S.
17
2008
Evaluation of two convolution sums involving the sum of divisors function. Zbl 1163.11301
Lemire, Mathieu; Williams, Kenneth S.
15
2006
Fourier series of a class of eta quotients. Zbl 1252.11043
Williams, Kenneth S.
15
2012
Mertens’ theorem for arithmetic progressions. Zbl 0286.10022
Williams, Kenneth S.
15
1974
Calculation of the class numbers of imaginary cyclic quartic fields. Zbl 0624.12004
Hardy, Kenneth; Hudson, R. H.; Richman, D.; Williams, Kenneth S.; Holtz, N. M.
14
1987
The number of representations of a positive integer by certain quaternary quadratic forms. Zbl 1221.11097
Alaca, Ayşe; Alaca, Şaban; Lemire, Mathieu F.; Williams, Kenneth S.
12
2009
Evaluation of some convolutions sums involving the sum of divisors functions. Zbl 1094.11004
Cheng, Nathalie; Williams, Kenneth S.
11
2005
Fourteen octonary quadratic forms. Zbl 1228.11049
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
10
2010
Jacobi’s identity and representations of integers by certain quaternary quadratic forms. Zbl 1209.11040
Alaca, Ayşe; Alaca, Şaban; Lemire, Mathieu F.; Williams, Kenneth S.
10
2007
Some series representations of \(\zeta(2n+1)\). Zbl 0808.11053
Zhang, Nanyue; Williams, Kenneth S.
10
1993
On the number of representations of \(n\) by \(ax^2+bxy+cy^2\). Zbl 1095.11024
Sun, Zhihong; Williams, Kenneth S.
9
2006
Binomial coefficients and Jacobi sums. Zbl 0551.12015
Hudson, Richard H.; Williams, Kenneth S.
9
1984
Pascal’s triangle (mod 8). Zbl 0889.11007
Huard, James G.; Spearman, Blair K.; Williams, Kenneth S.
9
1998
Evaluation of character sums connected with elliptic curves. Zbl 0369.10025
Williams, Kenneth S.
8
1979
Note on Salie’s sum. Zbl 0224.10039
Williams, Kenneth S.
8
1971
Evaluation of two trigonometric sums. Zbl 0820.11010
Williams, Kenneth S.; Zhang, Nan-Yue
8
1994
The integers of a cyclic quartic field. Zbl 0707.11078
Hudson, R. H.; Williams, K. S.
8
1990
Pell’s equations \(X^ 2-mY^ 2=-1,-4\) and continued fractions. Zbl 0596.10013
Kaplan, Pierre; Williams, Kenneth S.
8
1986
Congruences for \(L\)-functions. Zbl 0972.11001
Urbanowicz, Jerzy; Williams, Kenneth S.
8
2000
The Chowla-Selberg formula for genera. Zbl 0855.11018
Huard, James G.; Kaplan, Pierre; Williams, Kenneth S.
8
1995
An Artin character and representations of primes by binary quadratic forms. II. Zbl 0485.12003
Halter-Koch, Franz; Kaplan, Pierre; Williams, Kenneth S.
8
1982
The cyclotomic numbers of order seven. Zbl 0311.12008
Leonard, Philip A.; Williams, Kenneth S.
8
1975
Special values of the Lerch zeta function and the evaluation of certain integrals. Zbl 0785.11046
Williams, Kenneth S.; Zhang, Nanyue
8
1993
On \[ \sum_{n=1}^ \infty (1/n^{2k}) \]. Zbl 0224.40008
Williams, Kenneth S.
7
1971
\(A_4\)-sextic fields with a power basis. Zbl 1229.11136
Eloff, Daniel; Spearman, Blair K.; Williams, Kenneth S.
7
2007
Theta function identities and representations by certain quaternary quadratic forms. II. Zbl 1209.11041
Alaca, Ayşe; Alaca, Şaban; Lemire, Mathieu F.; Williams, Kenneth S.
7
2008
Seven octonary quadratic forms. Zbl 1171.11021
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
7
2008
Application of the Hurwitz zeta function to the evaluation of certain integrals. Zbl 0791.11045
Zhang, Nanyue; Williams, Kenneth S.
7
1993
On the imaginary bicyclic biquadratic fields with class-number 2. Zbl 0379.12002
Buell, D. A.; Williams, H. C.; Williams, K. S.
7
1977
Determination of all imaginary cyclic quartic fields with class number 2. Zbl 0678.12003
Hardy, Kenneth; Hudson, Richard H.; Richman, David; Williams, Kenneth S.
7
1989
Some Lambert series expansions of products of theta functions. Zbl 0938.11017
Williams, Kenneth S.
7
1999
The simplest arithmetic proof of Jacobi’s four squares theorem. Zbl 0958.11029
Spearman, Blair K.; Williams, Kenneth S.
7
2000
Values of the Riemann zeta functions and integrals involving \(\log (2\sinh {\theta\over 2})\) and \(\log (2\sin {\theta\over 2})\). Zbl 0828.11041
Zhang, Nan-Yue; Williams, Kenneth S.
7
1995
Class numbers and biquadratic reciprocity. Zbl 0473.12004
Williams, Kenneth S.; Currie, James D.
7
1982
Convolution sums involving the divisor function. Zbl 1156.11301
Cheng, Nathalie; Williams, Kenneth S.
7
2004
Quartics over GF(2\(^n\)). Zbl 0274.12013
Leonard, Philip A.; Williams, Kenneth S.
7
1973
On a double series of Chan and Ong. Zbl 1163.11318
Williams, Kenneth S.
7
2006
Some arithmetic identities involving divisor functions. Zbl 1318.11001
Alaca, Şaban; Uygul, Faruk; Williams, Kenneth S.
7
2012
A deterministic algorithm for solving \(n=fu^ 2+gv^ 2\) in coprime integers u and v. Zbl 0713.11088
Hardy, Kenneth; Muskat, Joseph B.; Williams, Kenneth S.
6
1990
Values of the Dedekind eta function at quadratic irrationalities. Zbl 0936.11026
van der Poorten, Alfred; Williams, Kenneth S.
6
1999
On two conjectures of Chowla. Zbl 0186.09301
Williams, Kenneth S.
6
1969
The quadratic and quartic character of certain quadratic units. II. Zbl 0386.12002
Leonard, Philip A.; Williams, Kenneth S.
6
1979
Relative integral bases for quartic fields over quadratic subfields. Zbl 0853.11090
Spearman, B. K.; Williams, K. S.
6
1996
On the class number of \(Q(\sqrt{-p})\) modulo 16, for \(p\equiv 1\) (mod 8) a prime. Zbl 0393.12008
Williams, Kenneth S.
6
1981
On the divisibility of the class numbers of \(\mathbb{Q}(\sqrt{-p})\) and \(\mathbb{Q}(\sqrt{-2p})\) by 16. Zbl 0431.12007
Leonard, Philip A.; Williams, Kenneth S.
6
1982
Some new residuacity criteria. Zbl 0456.10001
Hudson, Richard H.; Williams, Kenneth S.
6
1980
The septic character of \(2, 3, 5\) and \(7\). Zbl 0265.10004
Leonard, Philip A.; Williams, Kenneth S.
6
1974
On Euler’s criterion for cubic nonresidues. Zbl 0273.10002
Williams, Kenneth S.
6
1975
A rational octic reciprocity law. Zbl 0311.10004
Williams, Kenneth S.
6
1976
The quadratic and quartic character of certain quadratic units. I. Zbl 0335.12006
Leonard, Philip A.; Williams, Kenneth S.
6
1977
Dihedral quintic fields with a power basis. Zbl 1161.11393
Lavallee, Melissa J.; Spearman, Blair K.; Williams, Kenneth S.; Yang, Qiduan
5
2005
An upper bound for the sum \(\sum_{n=a+1}^{a+H}f(n)\) for a certain class of functions \(f\). Zbl 0743.11042
Dobrowolski, Edward; Williams, Kenneth S.
5
1992
The distribution of solutions of congruences. Zbl 0158.29603
Chalk, John H. H.; Williams, K. S.
5
1965
On exceptional polynomials. Zbl 0159.05304
Williams, K. S.
5
1968
The distribution of the residues of a quartic polynomial. Zbl 0171.00702
McCann, K.; Williams, K. S.
5
1967
On the quaternary forms \(x^2+y^2+z^2+5t^2\), \(x^2+y^2+5z^2+5t^2\) and \(x^2+5y^2+5z^2+5t^2\). Zbl 1196.11058
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
5
2007
An arithmetic proof of Jacobi’s eight squares theorem. Zbl 1004.11017
Williams, Kenneth S.
5
2001
Calculation of the class numbers of imaginary cyclic quartic fields. Zbl 0615.12009
Hardy, K.; Hudson, R. H.; Richman, D.; Williams, K. S.; Holtz, N. M.
5
1986
On the evaluation of the Legendre symbol \(((A+B\sqrt{m})/p)\). Zbl 0524.10002
Williams, Kenneth S.; Hardy, Kenneth; Friesen, Christian
5
1985
The index of a cyclic quartic field. Zbl 1049.11111
Spearman, Blair K.; Williams, Kenneth S.
5
2003
A “four integers” theorem and a “five integers” theorem. Zbl 1327.11024
Williams, Kenneth S.
5
2015
Note on Dickson’s permutation polynomials. Zbl 0235.12011
Williams, Kenneth S.
5
1971
On the number of distinguished representations of a group element. Zbl 0248.20018
Jacobson, David; Williams, Kenneth S.
5
1972
The cyclotomic numbers of order eleven. Zbl 0267.12009
Leonard, Philip A.; Williams, Kenneth S.
5
1975
A rational sixteenth power reciprocity law. Zbl 0363.10003
Leonard, Philip A.; Williams, Kenneth S.
5
1977
Pascal’s triangle mod 9. Zbl 0874.11024
Huard, James G.; Spearman, Blair K.; Williams, Kenneth S.
4
1997
On Scholz’s reciprocity law. Zbl 0372.12004
Williams, Kenneth S.
4
1977
Extensions of theorems of Cunningham-Aigner and Hasse-Evans. Zbl 0505.10001
Hudson, Richard H.; Williams, Kenneth S.
4
1983
Finite transformation formulae involving the Legendre symbol. Zbl 0207.05501
Williams, K. S.
4
1970
The simplest \(D_4\)-octics. Zbl 1144.11074
Spearman, Blair K.; Williams, Kenneth S.
4
2008
On the representations of a positive integer by the forms \(x^2+y^2+z^2+2t^2\) and \(x^2+2y^2+2z^2+2t^2\). Zbl 1213.11089
Williams, Kenneth S.
4
2008
On Liouville’s twelve squares theorem. Zbl 1242.11029
Williams, Kenneth S.
4
2008
Cubic fields with index 2. Zbl 0992.11058
Spearman, Blair K.; Williams, Kenneth S.
4
2002
A restricted Epstein zeta function and the evaluation of some definite integrals. Zbl 1037.11023
Muzaffar, Habib; Williams, Kenneth S.
4
2002
Cyclotomy of order 15 over \(GF(p^ 2)\), \(p=4,11\) (mod 15). Zbl 0611.12016
Friesen, Christian; Muskat, Joseph B.; Spearman, Blair K.; Williams, Kenneth S.
4
1986
Congruences modulo 16 for the class numbers of the quadratic fields \(Q(\sqrt{\pm p})\) and \(Q(\sqrt{\pm 2p})\) for \(p\) a prime congruent to 5 modulo 8. Zbl 0513.12007
Kaplan, Pierre; Williams, Kenneth S.
4
1982
A congruence relating the class numbers of complex quadratic fields. Zbl 0557.12003
Hardy, Kenneth; Williams, Kenneth S.
4
1986
Characterization of solvable quintics \(x^ 5+ ax+ b\). Zbl 0844.12002
Spearman, Blair K.; Williams, Kenneth S.
4
1994
Some new theta function identities with applications to sextenary quadratic forms. Zbl 1235.11039
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
4
2009
On the class numbers of \(Q(\sqrt{\pm 2p})\) modulo 16, for \(p=1 (\mod 8)\) a prime. Zbl 0491.12003
Kaplan, Pierre; Williams, Kenneth S.
4
1982
Derivable quadratic forms and representation numbers. Zbl 1478.11056
Aygin, Zafer Selcuk; Williams, Kenneth S.
1
2021
Prime-universal quadratic forms \(ax^2+by^2+cz^2\) and \(ax^2+by^2+cz^2+dw^2\). Zbl 1445.11021
Doyle, Greg; Williams, Kenneth S.
1
2020
Positive integers represented by regular primitive positive-definite integral ternary quadratic forms. Zbl 1467.11040
Doyle, Greg; Muskat, Joseph B.; Pehlivan, Lerna; Williams, Kenneth S.
1
2019
Evaluation of some \(q\)-integrals in terms of the Dedekind eta function. Zbl 1429.11079
Doyle, Greg; Williams, Kenneth S.
1
2018
\((k,l)\)-universality of ternary quadratic forms \(ax^2 + by^2 + cz^2\). Zbl 1450.11032
Pehlivan, Lerna; Williams, Kenneth S.
1
2018
Everything you wanted to know about \(ax^2+by^2+cz^2+dt^2\) but were afraid to ask. Zbl 1440.11047
Williams, Kenneth S.
1
2018
Some arithmetic convolution identities. Zbl 1422.11007
Williams, Kenneth S.
3
2017
Infinite products with coefficients which vanish on certain arithmetic progressions. Zbl 1429.11078
Alaca, Ayşe; Alaca, Şaban; Aygin, Zafer Selcuk; Williams, Kenneth S.
1
2017
A positive-definite ternary quadratic form does not represent all positive integers. Zbl 1412.11065
Doyle, Greg; Williams, Kenneth S.
1
2017
Representation numbers of certain quaternary quadratic forms in a genus consisting of a single class. Zbl 1350.11050
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
1
2016
A “four integers” theorem and a “five integers” theorem. Zbl 1327.11024
Williams, Kenneth S.
5
2015
Ternary quadratic forms and eta quotients. Zbl 1336.11033
Williams, Kenneth S.
2
2015
Historical remark on Ramanujan’s tau function. Zbl 1336.11037
Williams, Kenneth S.
1
2015
Double Gauss sums. Zbl 1366.11092
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
2
2014
The power series expansion of certain infinite products
\(q^{r}\prod_{n=1}^{\infty}(1-q^{n})^{a_{1}}(1-q^{2n})^{a_{2}}\cdots(1-q^{mn})^{a_{m}}\).
 Zbl 1285.11064
Pehlivan, Lerna; Williams, Kenneth S.
2
2014
On the number of representations of a positive integer as a sum of two binary quadratic forms. Zbl 1302.11013
Alaca, Şaban; Pehlivan, Lerna; Williams, Kenneth S.
2
2014
Ternary quadratic forms \(ax^2+by^2+cz^2\) representing all positive integers \(8k+4\). Zbl 1327.11023
Williams, Kenneth S.
1
2014
Quadratic forms and a product-to-sum formula. Zbl 1278.11043
Williams, Kenneth S.
3
2013
The parents of Jacobi’s four squares theorem are unique. Zbl 1305.11026
Williams, Kenneth S.
2
2013
Fourier series of a class of eta quotients. Zbl 1252.11043
Williams, Kenneth S.
15
2012
Some arithmetic identities involving divisor functions. Zbl 1318.11001
Alaca, Şaban; Uygul, Faruk; Williams, Kenneth S.
7
2012
On the quaternary forms \(x^2+y^2+2z^2+3t^2\), \(x^2+2y^2+2z^2+6t^2\), \(x^2+3y^2+3z^2+6t^2\) and \(2x^2+3y^2+6z^2+6t^2\). Zbl 1255.11020
Alaca, Ayşe; Williams, Kenneth S.
3
2012
Some product-to-sum identities. Zbl 1282.11039
Alaca, Şaban; Pehlivan, Lerna; Williams, Kenneth S.
1
2012
Number theory in the spirit of Liouville. Zbl 1227.11002
Williams, Kenneth S.
42
2011
Restricted Eisenstein series and certain convolution sums. Zbl 1245.11095
Alaca, Ayşe; Alaca, Şaban; Uygul, Faruk; Williams, Kenneth S.
2
2011
Lifting monogenic cubic fields to monogenic sextic fields. Zbl 1237.11045
Lavallee, Melisa J.; Spearman, Blair K.; Williams, Kenneth S.
2
2011
The number of representations of a positive integer by certain octonary quadratic forms. Zbl 1213.11087
Alaca, Şaban; Williams, Kenneth S.
25
2010
Fourteen octonary quadratic forms. Zbl 1228.11049
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
10
2010
Sextenary quadratic forms and an identity of Klein and Fricke. Zbl 1228.11050
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
3
2010
Representations by sextenary quadratic forms whose coefficients are 1, 2 and 4. Zbl 1213.11085
Alaca, Ayşe; Alaca, Şaban; Uygul, Faruk; Williams, Kenneth S.
2
2010
The number of representations of a positive integer by certain quaternary quadratic forms. Zbl 1221.11097
Alaca, Ayşe; Alaca, Şaban; Lemire, Mathieu F.; Williams, Kenneth S.
12
2009
Some new theta function identities with applications to sextenary quadratic forms. Zbl 1235.11039
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
4
2009
Some infinite products of Ramanujan type. Zbl 1234.11141
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
3
2009
Sums of \(4k\) squares: a polynomial approach. Zbl 1239.11044
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
2
2009
The convolution sum \(\sum_{m<n/16}\sigma(m)\sigma(n-16m)\). Zbl 1132.11305
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
26
2008
Theta functions identities and representations by certain quaternary quadratic forms. Zbl 1163.11029
Alaca, Ayşe; Alaca, Şaban; Lemire, Mathieu F.; Williams, Kenneth S.
17
2008
Theta function identities and representations by certain quaternary quadratic forms. II. Zbl 1209.11041
Alaca, Ayşe; Alaca, Şaban; Lemire, Mathieu F.; Williams, Kenneth S.
7
2008
Seven octonary quadratic forms. Zbl 1171.11021
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
7
2008
The simplest \(D_4\)-octics. Zbl 1144.11074
Spearman, Blair K.; Williams, Kenneth S.
4
2008
On the representations of a positive integer by the forms \(x^2+y^2+z^2+2t^2\) and \(x^2+2y^2+2z^2+2t^2\). Zbl 1213.11089
Williams, Kenneth S.
4
2008
On Liouville’s twelve squares theorem. Zbl 1242.11029
Williams, Kenneth S.
4
2008
Liouville’s sextenary quadratic forms \(x^2+y^2+z^2+t^2+2u^2+2v^2, x^2+y^2+2z^2+2t^2+2u^2+2v^2 \) and \(x^2 +2y^2+2z^2+2t^2+2u^2+4v^2\). Zbl 1213.11086
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
3
2008
Indices of integers in cyclic cubic fields. Zbl 1247.11135
Spearman, B. K.; Williams, K. S.
2
2008
Arithmetic progressions and binary quadratic forms. Zbl 1204.11073
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
1
2008
Evaluation of the convolution sums \(\sum _{l+6m=n}\sigma (l)\sigma (m)\) and \(\sum _{2l+3m=n}\sigma (l)\sigma (m)\). Zbl 1169.11002
Alaca, Şaban; Williams, Kenneth S.
35
2007
Nineteen quaternary quadratic forms. Zbl 1131.11025
Alaca, Ayşe; Alaca, Şaban; Lemire, Mathieu F.; Williams, Kenneth S.
30
2007
Evaluation of the convolution sums \(\sum_{l+18m=n}\sigma(l)\sigma(m)\) and \(\sum_{2l+9m=n}\sigma(l)\sigma(m)\). Zbl 1163.11003
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
26
2007
Evaluation of the convolution sums \(\sum_{l+24m=n}\sigma(l)\sigma(m)\) and \(\sum_{3l+8m=n}\sigma(l)\sigma(m)\). Zbl 1132.11304
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
19
2007
Jacobi’s identity and representations of integers by certain quaternary quadratic forms. Zbl 1209.11040
Alaca, Ayşe; Alaca, Şaban; Lemire, Mathieu F.; Williams, Kenneth S.
10
2007
\(A_4\)-sextic fields with a power basis. Zbl 1229.11136
Eloff, Daniel; Spearman, Blair K.; Williams, Kenneth S.
7
2007
On the quaternary forms \(x^2+y^2+z^2+5t^2\), \(x^2+y^2+5z^2+5t^2\) and \(x^2+5y^2+5z^2+5t^2\). Zbl 1196.11058
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
5
2007
Lambert series and Liouville’s identities. Zbl 1113.11004
Alaca, A.; Alaca, Ş.; McAfee, E.; Williams, K. S.
3
2007
An infinite class of identies. Zbl 1115.33017
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
1
2007
The simplest proof of Jacobi’s six squares theorem. Zbl 1204.11072
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
1
2007
The convolution sum \(\sum_{m<n/8} \sigma(m) \sigma(n-8m)\). Zbl 1130.11006
Williams, Kenneth S.
30
2006
Evaluation of the convolution sums \(\sum_{l+12m=n}\sigma(l)\sigma(m)\) and \(\sum_{3l+4m=n}\sigma(l)\sigma(m)\). Zbl 1154.11003
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
24
2006
On the two-dimensional theta functions of the Borweins. Zbl 1127.11035
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
23
2006
Evaluation of two convolution sums involving the sum of divisors function. Zbl 1163.11301
Lemire, Mathieu; Williams, Kenneth S.
15
2006
On the number of representations of \(n\) by \(ax^2+bxy+cy^2\). Zbl 1095.11024
Sun, Zhihong; Williams, Kenneth S.
9
2006
On a double series of Chan and Ong. Zbl 1163.11318
Williams, Kenneth S.
7
2006
Values of the Euler phi function not divisible by a given odd prime. Zbl 1216.11089
Spearman, Blair K.; Williams, Kenneth S.
3
2006
Ramanujan identities and Euler products for a type of Dirichlet series. Zbl 1155.11026
Sun, Zhihong; Williams, Kenneth S.
3
2006
\(\text{PSL}(2,5)\) sextic fields with a power basis. Zbl 1096.11038
Spearman, Blair K.; Watanabe, Aya; Williams, Kenneth S.
2
2006
Cyclic cubic fields of given conductor and given index. Zbl 1104.11047
Silvester, Alan K.; Spearman, Blair K.; Williams, Kenneth S.
2
2006
Evaluation of complete elliptic integrals of the first kind at singular moduli. Zbl 1139.11025
Muzaffar, Habib; Williams, Kenneth S.
2
2006
Cyclic quartic fields with a unique normal integral basis. Zbl 1172.11038
Spearman, Blair K.; Williams, Kenneth S.
1
2006
The convolution sum \(\sum_{m<n/9}\sigma(m)\sigma(n-9m)\). Zbl 1082.11003
Williams, Kenneth S.
25
2005
Evaluation of some convolutions sums involving the sum of divisors functions. Zbl 1094.11004
Cheng, Nathalie; Williams, Kenneth S.
11
2005
Dihedral quintic fields with a power basis. Zbl 1161.11393
Lavallee, Melissa J.; Spearman, Blair K.; Williams, Kenneth S.; Yang, Qiduan
5
2005
Watson’s method of solving a quintic equation. Zbl 1102.12001
Lavallee, Melisa J.; Spearman, Blair K.; Williams, Kenneth S.
2
2005
Irreducible quartic polynomials with factorization modulo \(p\). Zbl 1211.11037
Driver, Eric; Leonard, Philip A.; Williams, Kenneth S.
2
2005
Introductory algebraic number theory. Zbl 1035.11001
Alaca, Şaban; Williams, Kenneth S.
39
2004
Convolution sums involving the divisor function. Zbl 1156.11301
Cheng, Nathalie; Williams, Kenneth S.
7
2004
On the number of representations of a positive integer by a binary quadratic form. Zbl 1102.11024
Kaplan, Pierre; Williams, Kenneth S.
3
2004
Evaluation of Weber’s functions at quadratic irrationalities. Zbl 1077.11031
Muzaffar, Habib; Williams, Kenneth S.
2
2004
Normal integral bases for Emma Lehmer’s parametric family of cyclic quintics. Zbl 1158.11343
Spearman, Blair K.; Williams, Kenneth S.
2
2004
\(p\)-integral bases of a quartic field defined by a trinomial \(x^4+ax+b\). Zbl 1050.11091
Alaca, Şaban; Williams, Kenneth S.
1
2004
On Voronoi’s method for finding an integral basis of a cubic field. Zbl 1061.11056
Alaca, Şaban; Williams, Kenneth S.
1
2004
A cubic transformation formula for \(_{2}F_{1}(\frac{1}{3},\frac{2}{3};1;z)\) and some arithmetic convolution formulae. Zbl 1060.11003
Williams, Kenneth S.
1
2004
The factorization of 2 in cubic fields with index 2. Zbl 1080.11079
Alaca, Saban; Spearman, Blair K.; Williams, Kenneth S.
1
2004
The index of a cyclic quartic field. Zbl 1049.11111
Spearman, Blair K.; Williams, Kenneth S.
5
2003
The discriminant of a cyclic field of odd prime degree. Zbl 1074.11059
Spearman, Blair K.; Williams, Kenneth S.
3
2003
The index of a dihedral quartic field. Zbl 1049.11115
Silvester, Alan K.; Spearman, Blair K.; Williams, Kenneth S.
1
2003
\(n=\Delta +\Delta +2(\Delta + \Delta)\). Zbl 1041.11022
Williams, Kenneth S.
1
2003
Sums of twelve squares. Zbl 1023.11018
Huard, James G.; Williams, Kenneth S.
1
2003
Elementary evaluation of certain convolution sums involving divisor functions. Zbl 1062.11005
Huard, James G.; Ou, Zhiming M.; Spearman, Blair K.; Williams, Kenneth S.
47
2002
Cubic fields with index 2. Zbl 0992.11058
Spearman, Blair K.; Williams, Kenneth S.
4
2002
A restricted Epstein zeta function and the evaluation of some definite integrals. Zbl 1037.11023
Muzaffar, Habib; Williams, Kenneth S.
4
2002
The discriminant of a dihedral quintic field defined by a trinomial \(X^5+aX+b\). Zbl 1040.11076
Spearman, Blair K.; Williams, Kenneth S.
2
2002
The genera representing a positive integer. Zbl 0998.11018
Kaplan, Pierre; Williams, Kenneth S.
1
2002
An arithmetic proof of Jacobi’s eight squares theorem. Zbl 1004.11017
Williams, Kenneth S.
5
2001
The cubic congruence \(x^3+Ax^2+Bx+C\equiv 0\pmod p\) and binary quadratic forms. II. Zbl 1017.11017
Spearman, Blair K.; Williams, Kenneth S.
2
2001
Integers which are discriminants of bicyclic or cyclic quartic fields. Zbl 1038.11068
Spearman, Blair K.; Williams, Kenneth S.
1
2001
On the density of cyclic quartic fields. Zbl 0996.11068
Ou, Zhiming M.; Williams, Kenneth S.
1
2001
Congruences for \(L\)-functions. Zbl 0972.11001
Urbanowicz, Jerzy; Williams, Kenneth S.
8
2000
The simplest arithmetic proof of Jacobi’s four squares theorem. Zbl 0958.11029
Spearman, Blair K.; Williams, Kenneth S.
7
2000
Quartic trinomials with Galois groups \(A_4\) and \(V_4\). Zbl 0987.11063
Spearman, Blair K.; Williams, Kenneth S.
3
2000
Pure quintic fields defined by trinomials. Zbl 0970.11040
Spearman, Blair K.; Williams, Kenneth S.
2
2000
Some Lambert series expansions of products of theta functions. Zbl 0938.11017
Williams, Kenneth S.
7
1999
Values of the Dedekind eta function at quadratic irrationalities. Zbl 0936.11026
van der Poorten, Alfred; Williams, Kenneth S.
6
1999
...and 149 more Documents
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Cited by 1,060 Authors

68 Williams, Kenneth S.
24 Sun, Zhihong
22 Alaca, Şaban
20 Spearman, Blair Kenneth
17 Alaca, Ayşe
16 Evans, Ronald J.
15 Kim, Daeyeoul
14 Xia, Ernest X. W.
11 Aygin, Zafer Selçuk
11 Feng, Tao
10 Yao, Olivia Xiang Mei
9 Jones, Lenny K.
9 Srivastava, Hari Mohan
9 Ye, Dongxi
8 Dilcher, Karl
8 Halter-Koch, Franz
8 Zeng, Xiangyong
7 Berndt, Bruce Carl
7 Coffey, Mark William
7 Li, Chengju
7 Ramakrishnan, Balakrishnan
7 Sahu, Brundaban
7 Sun, Zhi-Wei
7 Tsumura, Hirofumi
7 Xiang, Qing
7 Yue, Qin
6 Baoulina, Ioulia N.
6 Barman, Rupam
6 Kim, Minsoo
6 Köklüce, Bülent
6 Louboutin, Stéphane R.
6 McCarthy, Dermot
6 Momihara, Koji
6 Tu, Ziran
5 Bibak, Khodakhast
5 Cao, Wei
5 Cho, Bumkyu
5 Cooper, Shaun
5 Gao, Peng
5 Garcia, Stephan Ramon
5 Helleseth, Tor
5 Hou, Xiang-Dong
5 Hu, Su
5 Hudson, Richard H.
5 Kaplan, Pierre
5 Kim, Aeran
5 Leonard, Philip A.
5 Moslehian, Mohammad Sal
5 Ntienjem, Ebénézer
5 Oh, Byeong-Kweon
5 Park, Yoon Kyung
5 Pehlivan, Lerna
5 Saikia, Neelam
5 Saito, Kichisuke
5 Singh, Anup Kumar
5 Wu, Hai-Liang
5 Zaharescu, Alexandru
5 Zhao, Liangyi
4 Cosgrave, John B.
4 Doyle, Greg
4 Feng, Keqin
4 Gurak, Stanley J.
4 Kapron, Bruce M.
4 Kim, Henry H.
4 Kwon, Soonhak
4 Luca, Florian
4 Mesnager, Sihem
4 Minculete, Nicusor
4 Moree, Pieter
4 Nakahara, Toru
4 Seeger, Alberto
4 Srinivasan, Venkatesh
4 Tanti, Jagmohan
4 Toh, Pee Choon
4 van Wamelen, Paul B.
4 Yang, Qiduan
3 Ahn, Jaehyun
3 Alahmadi, Adel N.
3 Ayad, Mohamed
3 Bayad, Abdelmejid
3 Blagouchine, Iaroslav V.
3 Bradley, David M.
3 Cai, Tianxin
3 Carlet, Claude
3 Chamberland, Marc
3 Chan, Heng Huat
3 Chern, Shane
3 Chou, Wunseng
3 Cochrane, Todd
3 Cvijović, Djurdje
3 Dadipour, Farzad
3 El Bachraoui, Mohamed
3 Farr, Ricky E.
3 Friedlander, John Benjamin
3 Gaál, István
3 Greene, John
3 Harrington, Joshua
3 Heng, Ziling
3 Hijazi, Rola Asaad
3 Huard, James G.
...and 960 more Authors
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Cited in 189 Serials

144 Journal of Number Theory
86 International Journal of Number Theory
53 Finite Fields and their Applications
40 The Ramanujan Journal
38 Proceedings of the American Mathematical Society
28 Journal of Mathematical Analysis and Applications
28 Mathematics of Computation
27 Designs, Codes and Cryptography
22 Journal de Théorie des Nombres de Bordeaux
20 Rocky Mountain Journal of Mathematics
19 Cryptography and Communications
16 Functiones et Approximatio. Commentarii Mathematici
14 Bulletin of the Australian Mathematical Society
13 Acta Arithmetica
12 Integers
11 Transactions of the American Mathematical Society
10 Discrete Mathematics
10 Advances in Mathematics
10 Manuscripta Mathematica
9 Archiv der Mathematik
9 Journal of Algebra
9 Linear Algebra and its Applications
9 Journal of Inequalities and Applications
8 Journal of Combinatorial Theory. Series A
8 Advances in Applied Mathematics
7 Communications in Algebra
7 Proceedings of the Japan Academy. Series A
6 Acta Mathematica Hungarica
6 Journal of Algebra and its Applications
5 Annales de l’Institut Fourier
5 Glasgow Mathematical Journal
5 International Journal of Mathematics and Mathematical Sciences
5 Applicable Algebra in Engineering, Communication and Computing
5 Journal of Algebraic Combinatorics
5 Research in Number Theory
4 Israel Journal of Mathematics
4 Journal of Computational and Applied Mathematics
4 Mathematische Annalen
4 Mathematische Zeitschrift
4 Tokyo Journal of Mathematics
4 European Journal of Combinatorics
4 Journal of the Ramanujan Mathematical Society
4 The Electronic Journal of Combinatorics
4 Abstract and Applied Analysis
4 Acta Mathematica Sinica. English Series
4 Advances in Difference Equations
4 Applicable Analysis and Discrete Mathematics
4 European Journal of Pure and Applied Mathematics
4 Science China. Mathematics
4 Afrika Matematika
3 American Mathematical Monthly
3 Discrete Applied Mathematics
3 Journal of Mathematical Physics
3 Mathematical Notes
3 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
3 Applied Mathematics and Computation
3 Compositio Mathematica
3 Inventiones Mathematicae
3 Journal of Combinatorial Theory. Series B
3 Kyungpook Mathematical Journal
3 Journal of Symbolic Computation
3 Forum Mathematicum
3 International Journal of Mathematics
3 Journal of Mathematical Sciences (New York)
3 Annals of Combinatorics
3 Nihonkai Mathematical Journal
3 Comptes Rendus. Mathématique. Académie des Sciences, Paris
3 Mediterranean Journal of Mathematics
3 Journal of Classical Analysis
3 Open Mathematics
2 Communications in Mathematical Physics
2 Indian Journal of Pure & Applied Mathematics
2 Nuclear Physics. B
2 Periodica Mathematica Hungarica
2 Ukrainian Mathematical Journal
2 Beiträge zur Algebra und Geometrie
2 Czechoslovak Mathematical Journal
2 Illinois Journal of Mathematics
2 Journal of the Korean Mathematical Society
2 Journal of the Mathematical Society of Japan
2 Journal of Pure and Applied Algebra
2 Kodai Mathematical Journal
2 Nagoya Mathematical Journal
2 Osaka Journal of Mathematics
2 Proceedings of the Edinburgh Mathematical Society. Series II
2 Results in Mathematics
2 Theoretical Computer Science
2 Geometric and Functional Analysis. GAFA
2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
2 New Zealand Journal of Mathematics
2 Kyushu Journal of Mathematics
2 Turkish Journal of Mathematics
2 The New York Journal of Mathematics
2 Acta Mathematica et Informatica Universitatis Ostraviensis
2 Doklady Mathematics
2 Honam Mathematical Journal
2 Mathematical Inequalities & Applications
2 Journal of the Australian Mathematical Society
2 Journal of Applied Mathematics
2 Journal of Applied Mathematics and Computing
...and 89 more Serials
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Cited in 44 Fields

844 Number theory (11-XX)
113 Combinatorics (05-XX)
82 Special functions (33-XX)
57 Information and communication theory, circuits (94-XX)
48 Field theory and polynomials (12-XX)
42 Algebraic geometry (14-XX)
33 Functional analysis (46-XX)
24 Real functions (26-XX)
19 Linear and multilinear algebra; matrix theory (15-XX)
19 Sequences, series, summability (40-XX)
15 Group theory and generalizations (20-XX)
15 Operator theory (47-XX)
14 Commutative algebra (13-XX)
14 Computer science (68-XX)
13 Functions of a complex variable (30-XX)
13 Harmonic analysis on Euclidean spaces (42-XX)
13 Quantum theory (81-XX)
8 Convex and discrete geometry (52-XX)
8 Numerical analysis (65-XX)
7 Order, lattices, ordered algebraic structures (06-XX)
7 Associative rings and algebras (16-XX)
7 Dynamical systems and ergodic theory (37-XX)
7 Approximations and expansions (41-XX)
7 Probability theory and stochastic processes (60-XX)
5 History and biography (01-XX)
5 Geometry (51-XX)
5 Manifolds and cell complexes (57-XX)
4 Nonassociative rings and algebras (17-XX)
4 Operations research, mathematical programming (90-XX)
3 General and overarching topics; collections (00-XX)
3 \(K\)-theory (19-XX)
3 Measure and integration (28-XX)
3 Ordinary differential equations (34-XX)
3 Global analysis, analysis on manifolds (58-XX)
3 Statistical mechanics, structure of matter (82-XX)
2 Category theory; homological algebra (18-XX)
2 Several complex variables and analytic spaces (32-XX)
2 Partial differential equations (35-XX)
2 Fluid mechanics (76-XX)
1 Abstract harmonic analysis (43-XX)
1 Integral equations (45-XX)
1 Calculus of variations and optimal control; optimization (49-XX)
1 Differential geometry (53-XX)
1 General topology (54-XX)

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