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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: Wiliams, Kenneth S.; Williams, K. S.; Williams, Kenneth S.; Williams, kenneth S.
Homepage: http://people.math.carleton.ca/~williams/index.html
External Links: MGP · dblp · GND
Documents Indexed: 379 Publications since 1964, including 13 Books
Reviewing Activity: 94 Reviews
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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
4 Indian Journal of Pure & Applied Mathematics
4 Journal für die Reine und Angewandte Mathematik
4 Utilitas Mathematica
4 The Ramanujan Journal
4 Integers
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 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 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

240 Publications have been cited 1,532 times in 920 Documents Cited by Year
Gauss and Jacobi sums. Zbl 0906.11001
Berndt, Bruce C.; Evans, Ronald J.; Williams, Kenneth S.
266
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.
43
2002
A simple norm inequality. Zbl 0178.16202
Dunkl, Charles F.; Williams, K. S.
40
1964
Number theory in the spirit of Liouville. Zbl 1227.11002
Williams, Kenneth S.
37
2011
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.
32
2007
Introductory algebraic number theory. Zbl 1035.11001
Alaca, Şaban; Williams, Kenneth S.
32
2004
Nineteen quaternary quadratic forms. Zbl 1131.11025
Alaca, Ayşe; Alaca, Şaban; Lemire, Mathieu F.; Williams, Kenneth S.
30
2007
The convolution sum \(\sum_{m<n/8} \sigma(m) \sigma(n-8m)\). Zbl 1130.11006
Williams, Kenneth S.
29
2006
Integers of biquadratic fields. Zbl 0205.35401
Williams, Kenneth S.
29
1970
The convolution sum \(\sum_{m<n/16}\sigma(m)\sigma(n-16m)\). Zbl 1132.11305
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
24
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.
24
2007
The convolution sum \(\sum_{m<n/9}\sigma(m)\sigma(n-9m)\). Zbl 1082.11003
Williams, Kenneth S.
24
2005
The number of representations of a positive integer by certain octonary quadratic forms. Zbl 1213.11087
Alaca, Şaban; Williams, Kenneth S.
23
2010
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.
23
2006
On the two-dimensional theta functions of the Borweins. Zbl 1127.11035
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
22
2006
Note on cubics over \(GF(2^n)\) and \(GF(3^n)\). Zbl 0321.12029
Williams, Kenneth S.
21
1975
On Tornheim’s double series. Zbl 0858.40008
Huard, James G.; Williams, Kenneth S.; Zhang, Nanyue
20
1996
Some results on the generalized Stieltjes constants. Zbl 0808.11054
Zhang, Nanyue; Williams, Kenneth S.
19
1994
Evaluation of two convolution sums involving the sum of divisors function. Zbl 1163.11301
Lemire, Mathieu; Williams, Kenneth S.
18
2006
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 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.
17
2007
Integral bases for quartic fields with quadratic subfields. Zbl 0826.11048
Huard, James G.; Spearman, Blair K.; Williams, Kenneth S.
17
1995
Fourier series of a class of eta quotients. Zbl 1252.11043
Williams, Kenneth S.
13
2012
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
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.
12
1987
Mertens’ theorem for arithmetic progressions. Zbl 0286.10022
Williams, Kenneth S.
12
1974
On the number of representations of \(n\) by \(ax^2+bxy+cy^2\). Zbl 1095.11024
Sun, Zhihong; Williams, Kenneth S.
11
2006
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
Fourteen octonary quadratic forms. Zbl 1228.11049
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
9
2010
Evaluation of some convolutions sums involving the sum of divisors functions. Zbl 1094.11004
Cheng, Nathalie; Williams, Kenneth S.
9
2005
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.
9
1995
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.
8
1998
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
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
Quartics over GF(2\(^n\)). Zbl 0274.12013
Leonard, Philip A.; Williams, Kenneth S.
8
1973
Note on Salie’s sum. Zbl 0224.10039
Williams, Kenneth S.
8
1971
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
Convolution sums involving the divisor function. Zbl 1156.11301
Cheng, Nathalie; Williams, Kenneth S.
7
2004
Congruences for \(L\)-functions. Zbl 0972.11001
Urbanowicz, Jerzy; Williams, Kenneth S.
7
2000
Some Lambert series expansions of products of theta functions. Zbl 0938.11017
Williams, Kenneth S.
7
1999
The Chowla-Selberg formula for genera. Zbl 0855.11018
Huard, James G.; Kaplan, Pierre; Williams, Kenneth S.
7
1995
Application of the Hurwitz zeta function to the evaluation of certain integrals. Zbl 0791.11045
Zhang, Nanyue; Williams, Kenneth S.
7
1993
Special values of the Lerch zeta function and the evaluation of certain integrals. Zbl 0785.11046
Williams, Kenneth S.; Zhang, Nanyue
7
1993
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
Evaluation of character sums connected with elliptic curves. Zbl 0369.10025
Williams, Kenneth S.
7
1979
On \[ \sum_{n=1}^ \infty (1/n^{2k}) \]. Zbl 0224.40008
Williams, Kenneth S.
7
1971
Some arithmetic identities involving divisor functions. Zbl 1318.11001
Alaca, Şaban; Uygul, Faruk; Williams, Kenneth S.
6
2012
Seven octonary quadratic forms. Zbl 1171.11021
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
6
2008
On a double series of Chan and Ong. Zbl 1163.11318
Williams, Kenneth S.
6
2006
The simplest arithmetic proof of Jacobi’s four squares theorem. Zbl 0958.11029
Spearman, Blair K.; Williams, Kenneth S.
6
2000
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
Some new residuacity criteria. Zbl 0456.10001
Hudson, Richard H.; Williams, Kenneth S.
6
1980
The quadratic and quartic character of certain quadratic units. II. Zbl 0386.12002
Leonard, Philip A.; Williams, Kenneth S.
6
1979
On the imaginary bicyclic biquadratic fields with class-number 2. Zbl 0379.12002
Buell, D. A.; Williams, H. C.; Williams, K. S.
6
1977
The quadratic and quartic character of certain quadratic units. I. Zbl 0335.12006
Leonard, Philip A.; Williams, Kenneth S.
6
1977
A rational octic reciprocity law. Zbl 0311.10004
Williams, Kenneth S.
6
1976
On Euler’s criterion for cubic nonresidues. Zbl 0273.10002
Williams, Kenneth S.
6
1975
The septic character of \(2, 3, 5\) and \(7\). Zbl 0265.10004
Leonard, Philip A.; Williams, Kenneth S.
6
1974
On two conjectures of Chowla. Zbl 0186.09301
Williams, Kenneth S.
6
1969
A “four integers” theorem and a “five integers” theorem. Zbl 1327.11024
Williams, Kenneth S.
5
2015
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
Dihedral quintic fields with a power basis. Zbl 1161.11393
Lavallee, Melissa J.; Spearman, Blair K.; Williams, Kenneth S.; Yang, Qiduan
5
2005
Values of the Dedekind eta function at quadratic irrationalities. Zbl 0936.11026
van der Poorten, Alfred; Williams, Kenneth S.
5
1999
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
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
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.
5
1982
Class numbers and biquadratic reciprocity. Zbl 0473.12004
Williams, Kenneth S.; Currie, James D.
5
1982
On the class number of \(Q(\sqrt{-p})\) modulo 16, for \(p\equiv 1\) (mod 8) a prime. Zbl 0393.12008
Williams, Kenneth S.
5
1981
A rational sixteenth power reciprocity law. Zbl 0363.10003
Leonard, Philip A.; Williams, Kenneth S.
5
1977
The cyclotomic numbers of order eleven. Zbl 0267.12009
Leonard, Philip A.; Williams, Kenneth S.
5
1975
On the number of distinguished representations of a group element. Zbl 0248.20018
Jacobson, David; Williams, Kenneth S.
5
1972
Note on Dickson’s permutation polynomials. Zbl 0235.12011
Williams, Kenneth S.
5
1971
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
The distribution of solutions of congruences. Zbl 0158.29603
Chalk, John H. H.; Williams, K. S.
5
1965
Some new theta function identities with applications to sextenary quadratic forms. Zbl 1235.11039
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
4
2009
On Liouville’s twelve squares theorem. Zbl 1242.11029
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
The simplest \(D_4\)-octics. Zbl 1144.11074
Spearman, Blair K.; Williams, Kenneth S.
4
2008
\(A_4\)-sextic fields with a power basis. Zbl 1229.11136
Eloff, Daniel; Spearman, Blair K.; Williams, Kenneth S.
4
2007
The index of a cyclic quartic field. Zbl 1049.11111
Spearman, Blair K.; Williams, Kenneth S.
4
2003
An arithmetic proof of Jacobi’s eight squares theorem. Zbl 1004.11017
Williams, Kenneth S.
4
2001
Pascal’s triangle mod 9. Zbl 0874.11024
Huard, James G.; Spearman, Blair K.; Williams, Kenneth S.
4
1997
On solvable quintics \(X^ 5 + aX +b\) and \(X^ 5 + aX^ 2 +b\). Zbl 0862.12002
Spearman, Blair K.; Williams, Kenneth S.
4
1996
A refinement of H. C. Williams’ \(q\)th root algorithm. Zbl 0782.11040
Williams, Kenneth S.; Hardy, Kenneth
4
1993
A congruence relating the class numbers of complex quadratic fields. Zbl 0557.12003
Hardy, Kenneth; Williams, Kenneth S.
4
1986
Extensions of theorems of Cunningham-Aigner and Hasse-Evans. Zbl 0505.10001
Hudson, Richard H.; Williams, Kenneth S.
4
1983
On Scholz’s reciprocity law. Zbl 0372.12004
Williams, Kenneth S.
4
1977
Note on a cubic character sum. Zbl 0307.10038
Williams, Kenneth S.
4
1975
Jacobi sums and a theorem of Brewer. Zbl 0297.10023
Leonard, Philip A.; Williams, Kenneth S.
4
1975
A Diophantine system of Dickson. Zbl 0299.12017
Leonard, Philip A.; Williams, Kenneth S.
4
1974
Finite transformation formulae involving the Legendre symbol. Zbl 0207.05501
Williams, K. S.
4
1970
Quadratic forms and a product-to-sum formula. Zbl 1278.11043
Williams, Kenneth S.
3
2013
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
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
Evaluation of some \(q\)-integrals in terms of the Dedekind eta function. Zbl 1429.11079
Doyle, Greg; Williams, Kenneth S.
1
2018
A positive-definite ternary quadratic form does not represent all positive integers. Zbl 1412.11065
Doyle, Greg; Williams, Kenneth S.
1
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
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
Double Gauss sums. Zbl 1366.11092
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
1
2014
Ternary quadratic forms \(ax^2+by^2+cz^2\) representing all positive integers \(8k+4\). Zbl 1327.11023
Williams, Kenneth S.
1
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.
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.
13
2012
Some arithmetic identities involving divisor functions. Zbl 1318.11001
Alaca, Şaban; Uygul, Faruk; Williams, Kenneth S.
6
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.
37
2011
Restricted Eisenstein series and certain convolution sums. Zbl 1245.11095
Alaca, Ayşe; Alaca, Şaban; Uygul, Faruk; 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.
23
2010
Fourteen octonary quadratic forms. Zbl 1228.11049
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
9
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
Sums of \(4k\) squares: a polynomial approach. Zbl 1239.11044
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
3
2009
Some infinite products of Ramanujan type. Zbl 1234.11141
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
3
2009
The convolution sum \(\sum_{m<n/16}\sigma(m)\sigma(n-16m)\). Zbl 1132.11305
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
24
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.
6
2008
On Liouville’s twelve squares theorem. Zbl 1242.11029
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
The simplest \(D_4\)-octics. Zbl 1144.11074
Spearman, Blair K.; 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
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.
32
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.
24
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.
17
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
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
\(A_4\)-sextic fields with a power basis. Zbl 1229.11136
Eloff, Daniel; Spearman, Blair K.; Williams, Kenneth S.
4
2007
Lambert series and Liouville’s identities. Zbl 1113.11004
Alaca, A.; Alaca, Ş.; McAfee, E.; Williams, K. S.
3
2007
The simplest proof of Jacobi’s six squares theorem. Zbl 1204.11072
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
1
2007
An infinite class of identies. Zbl 1115.33017
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.
29
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.
23
2006
On the two-dimensional theta functions of the Borweins. Zbl 1127.11035
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
22
2006
Evaluation of two convolution sums involving the sum of divisors function. Zbl 1163.11301
Lemire, Mathieu; Williams, Kenneth S.
18
2006
On the number of representations of \(n\) by \(ax^2+bxy+cy^2\). Zbl 1095.11024
Sun, Zhihong; Williams, Kenneth S.
11
2006
On a double series of Chan and Ong. Zbl 1163.11318
Williams, Kenneth S.
6
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
Evaluation of complete elliptic integrals of the first kind at singular moduli. Zbl 1139.11025
Muzaffar, Habib; 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
Cyclic quartic fields with a unique normal integral basis. Zbl 1172.11038
Spearman, Blair K.; Williams, Kenneth S.
1
2006
\(\text{PSL}(2,5)\) sextic fields with a power basis. Zbl 1096.11038
Spearman, Blair K.; Watanabe, Aya; Williams, Kenneth S.
1
2006
The convolution sum \(\sum_{m<n/9}\sigma(m)\sigma(n-9m)\). Zbl 1082.11003
Williams, Kenneth S.
24
2005
Evaluation of some convolutions sums involving the sum of divisors functions. Zbl 1094.11004
Cheng, Nathalie; Williams, Kenneth S.
9
2005
Dihedral quintic fields with a power basis. Zbl 1161.11393
Lavallee, Melissa J.; Spearman, Blair K.; Williams, Kenneth S.; Yang, Qiduan
5
2005
Irreducible quartic polynomials with factorization modulo \(p\). Zbl 1211.11037
Driver, Eric; Leonard, Philip A.; Williams, Kenneth S.
2
2005
Watson’s method of solving a quintic equation. Zbl 1102.12001
Lavallee, Melisa J.; Spearman, Blair K.; Williams, Kenneth S.
1
2005
Introductory algebraic number theory. Zbl 1035.11001
Alaca, Şaban; Williams, Kenneth S.
32
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
Normal integral bases for Emma Lehmer’s parametric family of cyclic quintics. Zbl 1158.11343
Spearman, Blair K.; Williams, Kenneth S.
2
2004
Evaluation of Weber’s functions at quadratic irrationalities. Zbl 1077.11031
Muzaffar, Habib; Williams, Kenneth S.
2
2004
The factorization of 2 in cubic fields with index 2. Zbl 1080.11079
Alaca, Saban; Spearman, Blair K.; 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
On Voronoi’s method for finding an integral basis of a cubic field. Zbl 1061.11056
Alaca, Şaban; Williams, Kenneth S.
1
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
The index of a cyclic quartic field. Zbl 1049.11111
Spearman, Blair K.; Williams, Kenneth S.
4
2003
The discriminant of a cyclic field of odd prime degree. Zbl 1074.11059
Spearman, Blair K.; Williams, Kenneth S.
2
2003
\(n=\Delta +\Delta +2(\Delta + \Delta)\). Zbl 1041.11022
Williams, Kenneth S.
1
2003
The index of a dihedral quartic field. Zbl 1049.11115
Silvester, Alan K.; Spearman, Blair K.; 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.
43
2002
Cubic fields with index 2. Zbl 0992.11058
Spearman, Blair K.; Williams, Kenneth S.
3
2002
A restricted Epstein zeta function and the evaluation of some definite integrals. Zbl 1037.11023
Muzaffar, Habib; Williams, Kenneth S.
2
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.
1
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.
4
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.
7
2000
The simplest arithmetic proof of Jacobi’s four squares theorem. Zbl 0958.11029
Spearman, Blair K.; Williams, Kenneth S.
6
2000
Pure quintic fields defined by trinomials. Zbl 0970.11040
Spearman, Blair K.; Williams, Kenneth S.
2
2000
Quartic trinomials with Galois groups \(A_4\) and \(V_4\). Zbl 0987.11063
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.
5
1999
Dihedral quintic polynomials and a theorem of Galois. Zbl 1056.12004
Spearman, Blair K.; Williams, Kenneth S.
1
1999
DeMoivre’s quintic and a theorem of Galois. Zbl 0964.11047
Spearman, Blair K.; Williams, Kenneth S.
1
1999
Gauss and Jacobi sums. Zbl 0906.11001
Berndt, Bruce C.; Evans, Ronald J.; Williams, Kenneth S.
266
1998
Pascal’s triangle (mod 8). Zbl 0889.11007
Huard, James G.; Spearman, Blair K.; Williams, Kenneth S.
8
1998
An explicit integral basis for a pure cubic field. Zbl 1069.11512
Spearman, Blair K.; Williams, Kenneth S.
2
1998
Pascal’s triangle mod 9. Zbl 0874.11024
Huard, James G.; Spearman, Blair K.; Williams, Kenneth S.
4
1997
On a formula of Dirichlet. Zbl 0934.11017
Kaplan, Pierre; Williams, Kenneth S.
2
1997
The conductor of a cyclic quartic field using Gauss sums. Zbl 0898.11041
Spearman, B. K.; Williams, K. S.
2
1997
Quadratic subfields of the splitting field of a dihedral quintic trinomial \(x^5+ax+b\). Zbl 0922.11092
Spearman, Blair K.; Spearman, Laura Y.; Williams, Kenneth S.
2
1997
...and 140 more Documents
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Cited by 986 Authors

67 Williams, Kenneth S.
23 Sun, Zhihong
22 Alaca, Şaban
20 Spearman, Blair Kenneth
17 Alaca, Ayşe
17 Evans, Ronald J.
13 Xia, Ernest X. W.
12 Feng, Tao
11 Kim, Daeyeoul
11 Momihara, Koji
11 Xiang, Qing
11 Yue, Qin
10 Li, Chengju
9 Aygin, Zafer Selçuk
9 Srivastava, Hari Mohan
9 Yao, Olivia Xiang Mei
9 Ye, Dongxi
8 Dilcher, Karl
8 Halter-Koch, Franz
8 Sun, Zhi-Wei
8 Zeng, Xiangyong
7 Baoulina, Ioulia N.
7 Coffey, Mark William
7 Tsumura, Hirofumi
6 Barman, Rupam
6 Berndt, Bruce Carl
6 Kokluce, Bulent
6 Louboutin, Stéphane R.
6 Ramakrishnan, Balakrishnan
6 Sahu, Brundaban
6 Tu, Ziran
5 Bibak, Khodakhast
5 Cao, Wei
5 Cho, Bumkyu
5 Cooper, Shaun
5 Helleseth, Tor
5 Heng, Ziling
5 Hudson, Richard H.
5 Jones, Lenny K.
5 Kaplan, Pierre
5 Kim, Aeran
5 Kim, Minsoo
5 Leonard, Philip A.
5 McCarthy, Dermot
5 Moslehian, Mohammad Sal
5 Park, Yoon Kyung
5 Saikia, Neelam
5 Saito, Kichisuke
4 Cosgrave, John B.
4 Feng, Keqin
4 Garcia, Stephan Ramon
4 Gurak, Stanley J.
4 Hou, Xiang-Dong
4 Hu, Su
4 Kapron, Bruce M.
4 Kim, Henry H.
4 Kwon, Soonhak
4 Luca, Florian
4 Moree, Pieter
4 Nakahara, Toru
4 Ntienjem, Ebénézer
4 Oh, Byeong-Kweon
4 Park, Ho-Jin
4 Pehlivan, Lerna
4 Seeger, Alberto
4 Singh, Anup Kumar
4 Srinivasan, Venkatesh
4 Toh, Pee Choon
4 van Wamelen, Paul B.
4 Yang, Jing
4 Yang, Qiduan
4 Zaharescu, Alexandru
3 Ahn, Jaehyun
3 Alahmadi, Adel N.
3 Ayad, Mohamed
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 Ding, Cunsheng
3 Doyle, Greg
3 El Bachraoui, Mohamed
3 Friedlander, John Benjamin
3 Gaál, István
3 Greene, John
3 Hijazi, Rola Asaad
3 Huard, James G.
3 Kendirli, Bariṣ
3 Kesicioğlu, Yavuz
3 Kihel, Omar
3 Kim, Chang Heon
3 Llorens-Fuster, Enrique
3 Merca, Mircea
...and 886 more Authors
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Cited in 178 Serials

145 Journal of Number Theory
84 International Journal of Number Theory
57 Finite Fields and their Applications
36 Proceedings of the American Mathematical Society
31 The Ramanujan Journal
27 Mathematics of Computation
25 Journal of Mathematical Analysis and Applications
25 Designs, Codes and Cryptography
20 Journal de Théorie des Nombres de Bordeaux
19 Rocky Mountain Journal of Mathematics
14 Cryptography and Communications
13 Functiones et Approximatio. Commentarii Mathematici
12 Bulletin of the Australian Mathematical Society
12 Discrete Mathematics
11 Journal of Combinatorial Theory. Series A
10 Acta Arithmetica
10 Manuscripta Mathematica
10 Integers
9 Archiv der Mathematik
9 Transactions of the American Mathematical Society
9 Linear Algebra and its Applications
8 Journal of Algebra
8 Journal of Inequalities and Applications
7 Advances in Mathematics
7 Proceedings of the Japan Academy. Series A
7 Advances in Applied Mathematics
6 Communications in Algebra
6 European Journal of Combinatorics
5 Annales de l’Institut Fourier
5 Acta Mathematica Hungarica
5 Applicable Algebra in Engineering, Communication and Computing
5 Journal of Algebraic Combinatorics
4 Israel Journal of Mathematics
4 Applied Mathematics and Computation
4 Glasgow Mathematical Journal
4 International Journal of Mathematics and Mathematical Sciences
4 Journal of Computational and Applied Mathematics
4 Mathematische Annalen
4 Mathematische Zeitschrift
4 Tokyo Journal of Mathematics
4 Abstract and Applied Analysis
4 Acta Mathematica Sinica. English Series
4 Journal of Algebra and its Applications
4 Advances in Difference Equations
4 European Journal of Pure and Applied Mathematics
4 Science China. Mathematics
4 Afrika Matematika
4 Research in Number Theory
3 Discrete Applied Mathematics
3 Journal of Mathematical Physics
3 Mathematical Notes
3 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
3 Compositio Mathematica
3 Inventiones Mathematicae
3 Journal of Combinatorial Theory. Series B
3 Kyungpook Mathematical Journal
3 Journal of Symbolic Computation
3 Journal of the Ramanujan Mathematical Society
3 Journal of Mathematical Sciences (New York)
3 Annals of Combinatorics
3 Nihonkai Mathematical Journal
3 Journal of Classical Analysis
2 American Mathematical Monthly
2 Communications in Mathematical Physics
2 Indian Journal of Pure & Applied Mathematics
2 Periodica Mathematica Hungarica
2 Ukrainian Mathematical Journal
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 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 Forum Mathematicum
2 International Journal of Mathematics
2 New Zealand Journal of Mathematics
2 Turkish Journal of Mathematics
2 The Electronic Journal of Combinatorics
2 Acta Mathematica et Informatica Universitatis Ostraviensis
2 Doklady Mathematics
2 Honam Mathematical Journal
2 Journal of Applied Mathematics
2 Comptes Rendus. Mathématique. Académie des Sciences, Paris
2 Journal of Applied Mathematics and Computing
2 Mediterranean Journal of Mathematics
2 Proceedings of the Japan Academy
2 Annales Mathématiques du Québec
2 Open Mathematics
2 Algebraic Combinatorics
1 Computers & Mathematics with Applications
1 Journal d’Analyse Mathématique
1 Lithuanian Mathematical Journal
1 The Mathematical Gazette
1 Nuclear Physics. B
1 Problems of Information Transmission
1 Reviews of Modern Physics
...and 78 more Serials
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Cited in 41 Fields

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

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