×

Williams, Kenneth S.

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.; Williams, Kenneth
Homepage: http://people.math.carleton.ca/~williams/index.html
External Links: MGP · dblp · GND
all top 5

Serials

33 Acta Arithmetica
27 Canadian Mathematical Bulletin
24 Proceedings of the American Mathematical Society
21 Far East Journal of Mathematical Sciences
16 American Mathematical Monthly
16 Journal of Number Theory
15 Pacific Journal of Mathematics
15 International Journal of Number Theory
14 Rocky Mountain Journal of Mathematics
13 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 Integers
6 Journal of Combinatorics and Number Theory
5 Archiv der Mathematik
5 The Ramanujan Journal
4 Bulletin of the Australian Mathematical Society
4 Indian Journal of Pure & Applied Mathematics
4 Journal für die Reine und Angewandte Mathematik
4 Utilitas Mathematica
3 Duke Mathematical Journal
3 Journal of the London Mathematical Society. Second Series
3 Kodai Mathematical Journal
3 Mathematical Journal of Okayama University
3 The Mathematics Student
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
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 Proceedings of the Japan Academy. Series A
1 Publicationes Mathematicae Debrecen
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 Turkish 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

265 Publications have been cited 2,158 times in 1,321 Documents Cited by Year
Gauss and Jacobi sums. Zbl 0906.11001
Berndt, Bruce C.; Evans, Ronald J.; Williams, Kenneth S.
405
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.
64
2002
Introductory algebraic number theory. Zbl 1035.11001
Alaca, Şaban; Williams, Kenneth S.
58
2004
A simple norm inequality. Zbl 0178.16202
Dunkl, Charles F.; Williams, K. S.
56
1964
Number theory in the spirit of Liouville. Zbl 1227.11002
Williams, Kenneth S.
56
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.
41
2007
Note on cubics over \(GF(2^n)\) and \(GF(3^n)\). Zbl 0321.12029
Williams, Kenneth S.
41
1975
Integers of biquadratic fields. Zbl 0205.35401
Williams, Kenneth S.
37
1970
The convolution sum \(\sum_{m<n/8} \sigma(m) \sigma(n-8m)\). Zbl 1130.11006
Williams, Kenneth S.
37
2006
Nineteen quaternary quadratic forms. Zbl 1131.11025
Alaca, Ayşe; Alaca, Şaban; Lemire, Mathieu F.; Williams, Kenneth S.
37
2007
The convolution sum \(\sum_{m<n/16}\sigma(m)\sigma(n-16m)\). Zbl 1132.11305
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
32
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.
32
2007
The convolution sum \(\sum_{m<n/9}\sigma(m)\sigma(n-9m)\). Zbl 1082.11003
Williams, Kenneth S.
31
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.
31
2006
The number of representations of a positive integer by certain octonary quadratic forms. Zbl 1213.11087
Alaca, Şaban; Williams, Kenneth S.
29
2010
Evaluation of two convolution sums involving the sum of divisors function. Zbl 1163.11301
Lemire, Mathieu; Williams, Kenneth S.
28
2006
On the two-dimensional theta functions of the Borweins. Zbl 1127.11035
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
27
2006
Some results on the generalized Stieltjes constants. Zbl 0808.11054
Zhang, Nanyue; Williams, Kenneth S.
25
1994
On Tornheim’s double series. Zbl 0858.40008
Huard, James G.; Williams, Kenneth S.; Zhang, Nanyue
24
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.
24
2007
Integral bases for quartic fields with quadratic subfields. Zbl 0826.11048
Huard, James G.; Spearman, Blair K.; Williams, Kenneth S.
23
1995
On the number of representations of \(n\) by \(ax^2+bxy+cy^2\). Zbl 1095.11024
Sun, Zhihong; Williams, Kenneth S.
21
2006
Quartics over GF(2\(^n\)). Zbl 0274.12013
Leonard, Philip A.; Williams, Kenneth S.
20
1973
Mertens’ theorem for arithmetic progressions. Zbl 0286.10022
Williams, Kenneth S.
20
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.
19
1987
Theta functions identities and representations by certain quaternary quadratic forms. Zbl 1163.11029
Alaca, Ayşe; Alaca, Şaban; Lemire, Mathieu F.; Williams, Kenneth S.
18
2008
Fourier series of a class of eta quotients. Zbl 1252.11043
Williams, Kenneth S.
17
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.
16
2009
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.
15
2007
Evaluation of some convolutions sums involving the sum of divisors functions. Zbl 1094.11004
Cheng, Nathalie; Williams, Kenneth S.
14
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.
13
1995
On \[ \sum_{n=1}^ \infty (1/n^{2k}) \]. Zbl 0224.40008
Williams, Kenneth S.
12
1971
Congruences for \(L\)-functions. Zbl 0972.11001
Urbanowicz, Jerzy; Williams, Kenneth S.
12
2000
The \(n\)th power of a \(2\times 2\) matrix. Zbl 0789.15015
Williams, Kenneth S.
12
1992
Some series representations of \(\zeta(2n+1)\). Zbl 0808.11053
Zhang, Nanyue; Williams, Kenneth S.
12
1993
Special values of the Lerch zeta function and the evaluation of certain integrals. Zbl 0785.11046
Williams, Kenneth S.; Zhang, Nanyue
12
1993
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.
11
1982
A restricted Epstein zeta function and the evaluation of some definite integrals. Zbl 1037.11023
Muzaffar, Habib; Williams, Kenneth S.
11
2002
\(A_4\)-sextic fields with a power basis. Zbl 1229.11136
Eloff, Daniel; Spearman, Blair K.; Williams, Kenneth S.
11
2007
Fourteen octonary quadratic forms. Zbl 1228.11049
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
11
2010
Evaluation of two trigonometric sums. Zbl 0820.11010
Williams, Kenneth S.; Zhang, Nan-Yue
10
1994
Binomial coefficients and Jacobi sums. Zbl 0551.12015
Hudson, Richard H.; Williams, Kenneth S.
10
1984
Theta function identities and representations by certain quaternary quadratic forms. II. Zbl 1209.11041
Alaca, Ayşe; Alaca, Şaban; Lemire, Mathieu F.; Williams, Kenneth S.
10
2008
Pascal’s triangle (mod 8). Zbl 0889.11007
Huard, James G.; Spearman, Blair K.; Williams, Kenneth S.
9
1998
The integers of a cyclic quartic field. Zbl 0707.11078
Hudson, R. H.; Williams, K. S.
9
1990
Some arithmetic identities involving divisor functions. Zbl 1318.11001
Alaca, Şaban; Uygul, Faruk; Williams, Kenneth S.
9
2012
The cyclotomic numbers of order seven. Zbl 0311.12008
Leonard, Philip A.; Williams, Kenneth S.
9
1975
Relative integral bases for quartic fields over quadratic subfields. Zbl 0853.11090
Spearman, B. K.; Williams, K. S.
9
1996
The Chowla-Selberg formula for genera. Zbl 0855.11018
Huard, James G.; Kaplan, Pierre; Williams, Kenneth S.
9
1995
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.
9
2007
Evaluation of character sums connected with elliptic curves. Zbl 0369.10025
Williams, Kenneth S.
9
1979
On the class number of \(Q(\sqrt{-p})\) modulo 16, for \(p\equiv 1\) (mod 8) a prime. Zbl 0393.12008
Williams, Kenneth S.
9
1981
Note on Salie’s sum. Zbl 0224.10039
Williams, Kenneth S.
8
1971
Dihedral quintic fields with a power basis. Zbl 1161.11393
Lavallee, Melissa J.; Spearman, Blair K.; Williams, Kenneth S.; Yang, Qiduan
8
2005
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
Pell’s equations \(X^ 2-mY^ 2=-1,-4\) and continued fractions. Zbl 0596.10013
Kaplan, Pierre; Williams, Kenneth S.
8
1986
Values of the Dedekind eta function at quadratic irrationalities. Zbl 0936.11026
van der Poorten, Alfred; Williams, Kenneth S.
8
1999
Some Lambert series expansions of products of theta functions. Zbl 0938.11017
Williams, Kenneth S.
8
1999
Determination of all imaginary cyclic quartic fields with class number 2. Zbl 0678.12003
Hardy, Kenneth; Hudson, Richard H.; Richman, David; Williams, Kenneth S.
8
1989
On the imaginary bicyclic biquadratic fields with class-number 2. Zbl 0379.12002
Buell, D. A.; Williams, H. C.; Williams, K. S.
8
1977
Convolution sums involving the divisor function. Zbl 1156.11301
Cheng, Nathalie; Williams, Kenneth S.
7
2004
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.
7
1990
On Euler’s criterion for cubic nonresidues. Zbl 0273.10002
Williams, Kenneth S.
7
1975
Class numbers and biquadratic reciprocity. Zbl 0473.12004
Williams, Kenneth S.; Currie, James D.
7
1982
The simplest arithmetic proof of Jacobi’s four squares theorem. Zbl 0958.11029
Spearman, Blair K.; Williams, Kenneth S.
7
2000
Application of the Hurwitz zeta function to the evaluation of certain integrals. Zbl 0791.11045
Zhang, Nanyue; Williams, Kenneth S.
7
1993
On a double series of Chan and Ong. Zbl 1163.11318
Williams, Kenneth S.
7
2006
Seven octonary quadratic forms. Zbl 1171.11021
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
7
2008
Note on Dickson’s permutation polynomials. Zbl 0235.12011
Williams, Kenneth S.
6
1971
Ramanujan identities and Euler products for a type of Dirichlet series. Zbl 1155.11026
Sun, Zhihong; Williams, Kenneth S.
6
2006
The distribution of solutions of congruences. Zbl 0158.29603
Chalk, John H. H.; Williams, K. S.
6
1965
On two conjectures of Chowla. Zbl 0186.09301
Williams, Kenneth S.
6
1969
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.
6
1992
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.
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
A rational octic reciprocity law. Zbl 0311.10004
Williams, Kenneth S.
6
1976
The index of a cyclic quartic field. Zbl 1049.11111
Spearman, Blair K.; Williams, Kenneth S.
6
2003
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.
6
1986
The simplest \(D_4\)-octics. Zbl 1144.11074
Spearman, Blair K.; Williams, Kenneth S.
6
2008
Values of the Euler phi function not divisible by a given odd prime. Zbl 1216.11089
Spearman, Blair K.; Williams, Kenneth S.
6
2006
The quadratic and quartic character of certain quadratic units. I. Zbl 0335.12006
Leonard, Philip A.; Williams, Kenneth S.
6
1977
The quadratic and quartic character of certain quadratic units. II. Zbl 0386.12002
Leonard, Philip A.; Williams, Kenneth S.
6
1979
A “four integers” theorem and a “five integers” theorem. Zbl 1327.11024
Williams, Kenneth S.
5
2015
\(p\)-integral bases of a quartic field defined by a trinomial \(x^4+ax+b\). Zbl 1050.11091
Alaca, Şaban; Williams, Kenneth S.
5
2004
On the number of distinguished representations of a group element. Zbl 0248.20018
Jacobson, David; Williams, Kenneth S.
5
1972
The distribution of the residues of a quartic polynomial. Zbl 0171.00702
McCann, K.; Williams, K. S.
5
1967
On exceptional polynomials. Zbl 0159.05304
Williams, K. S.
5
1968
\(\text{PSL}(2,5)\) sextic fields with a power basis. Zbl 1096.11038
Spearman, Blair K.; Watanabe, Aya; Williams, Kenneth S.
5
2006
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
A Diophantine system of Dickson. Zbl 0299.12017
Leonard, Philip A.; Williams, Kenneth S.
5
1974
On the evaluation of the Legendre symbol \(((A+B\sqrt{m})/p)\). Zbl 0524.10002
Williams, Kenneth S.; Hardy, Kenneth; Friesen, Christian
5
1985
Lifting monogenic cubic fields to monogenic sextic fields. Zbl 1237.11045
Lavallee, Melisa J.; Spearman, Blair K.; Williams, Kenneth S.
5
2011
Note on a result of Barrucand and Cohn. Zbl 0325.10002
Williams, Kenneth S.
5
1976
\(n=\Delta +\Delta +2(\Delta + \Delta)\). Zbl 1041.11022
Williams, Kenneth S.
5
2003
Some new theta function identities with applications to sextenary quadratic forms. Zbl 1235.11039
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
5
2009
An arithmetic proof of Jacobi’s eight squares theorem. Zbl 1004.11017
Williams, Kenneth S.
5
2001
Cubic fields with index 2. Zbl 0992.11058
Spearman, Blair K.; Williams, Kenneth S.
5
2002
Characterization of solvable quintics \(x^ 5+ ax+ b\). Zbl 0844.12002
Spearman, Blair K.; Williams, Kenneth S.
5
1994
Beyond the Basel problem. I. Zbl 07687521
Williams, Kenneth S.
1
2023
An application of binary quadratic forms of discriminant \(-31\) to modular forms. Zbl 1501.11056
Aygin, Zafer Selcuk; Williams, Kenneth S.
1
2022
Representation numbers of spinor regular ternary quadratic forms. Zbl 1506.11056
Aygin, Zafer Selcuk; Doyle, Greg; Münkel, Florian; Pehlivan, Lerna; Williams, Kenneth S.
2
2021
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
Representation numbers of seven quaternary quadratic forms each in a genus consisting of only two classes. Zbl 1493.11080
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth
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.
2
2019
\((k,l)\)-universality of ternary quadratic forms \(ax^2 + by^2 + cz^2\). Zbl 1450.11032
Pehlivan, Lerna; Williams, Kenneth S.
3
2018
Evaluation of some \(q\)-integrals in terms of the Dedekind eta function. Zbl 1429.11079
Doyle, Greg; 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
A positive-definite ternary quadratic form does not represent all positive integers. Zbl 1412.11065
Doyle, Greg; Williams, Kenneth S.
4
2017
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.
2
2017
A class of subsums of Euler’s sum. Zbl 1364.11009
Williams, Kenneth S.
2
2016
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
Bounds for the representations of integers by positive quadratic forms. Zbl 1398.11068
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 a theorem of Zhang and Yue. Zbl 1319.11076
Williams, Kenneth S.
1
2015
Historical remark on Ramanujan’s tau function. Zbl 1336.11037
Williams, Kenneth S.
1
2015
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.
4
2014
Double Gauss sums. Zbl 1366.11092
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
3
2014
Ternary quadratic forms \(ax^2+by^2+cz^2\) representing all positive integers \(8k+4\). Zbl 1327.11023
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
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
Euler products in Ramanujan’s lost notebook. Zbl 1281.11086
Berndt, Bruce C.; Kim, Byungchan; Williams, Kenneth S.
1
2013
Fourier series of a class of eta quotients. Zbl 1252.11043
Williams, Kenneth S.
17
2012
Some arithmetic identities involving divisor functions. Zbl 1318.11001
Alaca, Şaban; Uygul, Faruk; Williams, Kenneth S.
9
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.
4
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.
56
2011
Lifting monogenic cubic fields to monogenic sextic fields. Zbl 1237.11045
Lavallee, Melisa J.; Spearman, Blair K.; Williams, Kenneth S.
5
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.
29
2010
Fourteen octonary quadratic forms. Zbl 1228.11049
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
11
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.
16
2009
Some new theta function identities with applications to sextenary quadratic forms. Zbl 1235.11039
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
5
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.
3
2009
The convolution sum \(\sum_{m<n/16}\sigma(m)\sigma(n-16m)\). Zbl 1132.11305
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
32
2008
Theta functions identities and representations by certain quaternary quadratic forms. Zbl 1163.11029
Alaca, Ayşe; Alaca, Şaban; Lemire, Mathieu F.; Williams, Kenneth S.
18
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.
10
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.
6
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.
5
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.
41
2007
Nineteen quaternary quadratic forms. Zbl 1131.11025
Alaca, Ayşe; Alaca, Şaban; Lemire, Mathieu F.; Williams, Kenneth S.
37
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.
32
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.
24
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.
15
2007
\(A_4\)-sextic fields with a power basis. Zbl 1229.11136
Eloff, Daniel; Spearman, Blair K.; Williams, Kenneth S.
11
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.
9
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.
37
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.
31
2006
Evaluation of two convolution sums involving the sum of divisors function. Zbl 1163.11301
Lemire, Mathieu; Williams, Kenneth S.
28
2006
On the two-dimensional theta functions of the Borweins. Zbl 1127.11035
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
27
2006
On the number of representations of \(n\) by \(ax^2+bxy+cy^2\). Zbl 1095.11024
Sun, Zhihong; Williams, Kenneth S.
21
2006
On a double series of Chan and Ong. Zbl 1163.11318
Williams, Kenneth S.
7
2006
Ramanujan identities and Euler products for a type of Dirichlet series. Zbl 1155.11026
Sun, Zhihong; 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.
6
2006
\(\text{PSL}(2,5)\) sextic fields with a power basis. Zbl 1096.11038
Spearman, Blair K.; Watanabe, Aya; Williams, Kenneth S.
5
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
The prime ideal factorization of 2 in pure quartic fields with index 2. Zbl 1175.11061
Spearman, Blair K.; Williams, Kenneth S.
1
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.
31
2005
Evaluation of some convolutions sums involving the sum of divisors functions. Zbl 1094.11004
Cheng, Nathalie; Williams, Kenneth S.
14
2005
Dihedral quintic fields with a power basis. Zbl 1161.11393
Lavallee, Melissa J.; Spearman, Blair K.; Williams, Kenneth S.; Yang, Qiduan
8
2005
Irreducible quartic polynomials with factorization modulo \(p\). Zbl 1211.11037
Driver, Eric; Leonard, Philip A.; Williams, Kenneth S.
3
2005
Watson’s method of solving a quintic equation. Zbl 1102.12001
Lavallee, Melisa J.; Spearman, Blair K.; Williams, Kenneth S.
2
2005
Introductory algebraic number theory. Zbl 1035.11001
Alaca, Şaban; Williams, Kenneth S.
58
2004
Convolution sums involving the divisor function. Zbl 1156.11301
Cheng, Nathalie; Williams, Kenneth S.
7
2004
\(p\)-integral bases of a quartic field defined by a trinomial \(x^4+ax+b\). Zbl 1050.11091
Alaca, Şaban; Williams, Kenneth S.
5
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
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.
6
2003
\(n=\Delta +\Delta +2(\Delta + \Delta)\). Zbl 1041.11022
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
A relative integral basis over \(\mathbb{Q}(\sqrt{-3})\) for the normal closure of a pure cubic field. Zbl 1064.11070
Spearman, Blair K.; Williams, Kenneth S.
2
2003
Sums of twelve squares. Zbl 1023.11018
Huard, James G.; 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
Elementary evaluation of certain convolution sums involving divisor functions. Zbl 1062.11005
Huard, James G.; Ou, Zhiming M.; Spearman, Blair K.; Williams, Kenneth S.
64
2002
A restricted Epstein zeta function and the evaluation of some definite integrals. Zbl 1037.11023
Muzaffar, Habib; Williams, Kenneth S.
11
2002
Cubic fields with index 2. Zbl 0992.11058
Spearman, Blair K.; Williams, Kenneth S.
5
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.
3
2002
The genera representing a positive integer. Zbl 0998.11018
Kaplan, Pierre; Williams, Kenneth S.
1
2002
...and 165 more Documents
all top 5

Cited by 1,422 Authors

77 Williams, Kenneth S.
27 Sun, Zhihong
23 Alaca, Şaban
20 Spearman, Blair Kenneth
19 Alaca, Ayşe
19 Kim, Daeyeoul
17 Evans, Ronald J.
16 Sun, Zhi-Wei
15 Xia, Ernest X. W.
14 Barman, Rupam
13 Aygin, Zafer Selçuk
12 Jones, Lenny K.
11 Feng, Tao
11 Gao, Peng
11 Zeng, Xiangyong
11 Zhao, Liangyi
10 Saikia, Neelam
10 Yao, Olivia Xiang Mei
10 Ye, Dongxi
9 Köklüce, Bülent
9 McCarthy, Dermot
9 Ramakrishnan, Balakrishnan
9 Sahu, Brundaban
9 Srivastava, Hari Mohan
9 Xiang, Qing
9 Yue, Qin
8 Berndt, Bruce Carl
8 Dilcher, Karl
8 Halter-Koch, Franz
8 Helleseth, Tor
8 Pehlivan, Lerna
8 Wu, Hai-Liang
7 Baoulina, Ioulia N.
7 Coffey, Mark William
7 Li, Chengju
7 Momihara, Koji
7 Singh, Anup Kumar
7 Tripathi, Mohit
7 Tsumura, Hirofumi
6 Cao, Wei
6 Doyle, Greg
6 Hong, Shaofang
6 Kim, Minsoo
6 Li, Kangquan
6 Louboutin, Stéphane R.
6 Moree, Pieter
6 Park, Yoon Kyung
6 Qu, Longjiang
6 Sofo, Anthony
6 Tanti, Jagmohan
6 Tu, Ziran
6 Zaharescu, Alexandru
5 Batir, Necdet
5 Bibak, Khodakhast
5 Bringmann, Kathrin
5 Cho, Bumkyu
5 Cooper, Shaun
5 Feng, Keqin
5 Garcia, Stephan Ramon
5 Hou, Xiang-Dong
5 Hu, Su
5 Hudson, Richard H.
5 Kaplan, Pierre
5 Kim, Aeran
5 Kwon, Soonhak
5 Leonard, Philip A.
5 Mesnager, Sihem
5 Minculete, Nicusor
5 Moslehian, Mohammad Sal
5 Ntienjem, Ebénézer
5 Oh, Byeong-Kweon
5 Sahmoudi, Mohammed
5 Saito, Kichisuke
5 Toh, Pee Choon
4 Ahmed, Mohammad Helal Uddin
4 Azizi, Abdelmalek
4 Bayad, Abdelmejid
4 Blagouchine, Iaroslav V.
4 Chan, Heng Huat
4 Chems-Eddin, Mohamed Mahmoud
4 Cochrane, Todd
4 Cosgrave, John B.
4 Ding, Cunsheng
4 Gaál, István
4 Glasser, M. Lawrence
4 Gurak, Stanley J.
4 İkikardes, Nazli Yildiz
4 Kapron, Bruce M.
4 Kim, Henry H.
4 Li, Chunlei
4 Li, Nian
4 Llorens-Fuster, Enrique
4 Luca, Florian
4 Merca, Mircea
4 Mizuno, Yoshinori
4 Nakahara, Toru
4 Ono, Ken
4 Pauli, Sebastian
4 Saidak, Filip
4 Seeger, Alberto
...and 1,322 more Authors
all top 5

Cited in 258 Serials

159 Journal of Number Theory
101 International Journal of Number Theory
70 Finite Fields and their Applications
58 The Ramanujan Journal
39 Proceedings of the American Mathematical Society
35 Journal of Mathematical Analysis and Applications
30 Designs, Codes and Cryptography
29 Mathematics of Computation
25 Rocky Mountain Journal of Mathematics
23 Cryptography and Communications
22 Functiones et Approximatio. Commentarii Mathematici
22 Journal de Théorie des Nombres de Bordeaux
21 Integers
19 Bulletin of the Australian Mathematical Society
17 Acta Arithmetica
14 Journal of Combinatorial Theory. Series A
12 Discrete Mathematics
12 Advances in Mathematics
12 Transactions of the American Mathematical Society
10 Communications in Algebra
10 Journal of Algebra
10 Manuscripta Mathematica
10 Advances in Applied Mathematics
10 Journal of Algebra and its Applications
10 Research in Number Theory
9 Archiv der Mathematik
9 Linear Algebra and its Applications
9 Journal of Inequalities and Applications
8 Mathematische Annalen
7 Indian Journal of Pure & Applied Mathematics
7 Proceedings of the Japan Academy. Series A
7 European Journal of Combinatorics
7 Acta Mathematica Hungarica
7 Forum Mathematicum
7 Applicable Algebra in Engineering, Communication and Computing
7 Journal of Algebraic Combinatorics
7 Journal of Applied Mathematics & Informatics
6 Mathematische Zeitschrift
6 Research in the Mathematical Sciences
5 American Mathematical Monthly
5 Annales de l’Institut Fourier
5 Glasgow Mathematical Journal
5 International Journal of Mathematics and Mathematical Sciences
5 Journal of Computational and Applied Mathematics
5 Tokyo Journal of Mathematics
5 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
5 Turkish Journal of Mathematics
5 The Electronic Journal of Combinatorics
5 Journal of Integer Sequences
5 Mediterranean Journal of Mathematics
5 Advances in Difference Equations
5 Applicable Analysis and Discrete Mathematics
5 Science China. Mathematics
4 Israel Journal of Mathematics
4 Journal of Mathematical Physics
4 Applied Mathematics and Computation
4 Journal of Pure and Applied Algebra
4 Mathematica Slovaca
4 Monatshefte für Mathematik
4 Bulletin of the Korean Mathematical Society
4 Journal of the Ramanujan Mathematical Society
4 Abstract and Applied Analysis
4 Annals of Combinatorics
4 Acta Mathematica Sinica. English Series
4 Advances in Mathematics of Communications
4 European Journal of Pure and Applied Mathematics
4 Afrika Matematika
4 Journal of Classical Analysis
4 Open Mathematics
3 Discrete Applied Mathematics
3 Mathematical Notes
3 Periodica Mathematica Hungarica
3 Mathematics Magazine
3 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
3 Compositio Mathematica
3 Czechoslovak Mathematical Journal
3 Inventiones Mathematicae
3 Journal of Combinatorial Theory. Series B
3 Journal of the London Mathematical Society. Second Series
3 Kyungpook Mathematical Journal
3 Proceedings of the Edinburgh Mathematical Society. Series II
3 Proceedings of the London Mathematical Society. Third Series
3 Bulletin of the Iranian Mathematical Society
3 Journal of Symbolic Computation
3 International Journal of Mathematics
3 Expositiones Mathematicae
3 New Zealand Journal of Mathematics
3 Journal of Mathematical Sciences (New York)
3 Kyushu Journal of Mathematics
3 Filomat
3 Journal of Combinatorial Designs
3 Integral Transforms and Special Functions
3 Doklady Mathematics
3 Mathematical Inequalities & Applications
3 Nihonkai Mathematical Journal
3 Journal of Applied Mathematics
3 Comptes Rendus. Mathématique. Académie des Sciences, Paris
3 AIMS Mathematics
2 Communications in Mathematical Physics
2 Nuclear Physics. B
...and 158 more Serials
all top 5

Cited in 53 Fields

1,113 Number theory (11-XX)
154 Combinatorics (05-XX)
123 Special functions (33-XX)
77 Information and communication theory, circuits (94-XX)
58 Field theory and polynomials (12-XX)
53 Algebraic geometry (14-XX)
44 Functional analysis (46-XX)
29 Real functions (26-XX)
24 Linear and multilinear algebra; matrix theory (15-XX)
24 Sequences, series, summability (40-XX)
22 Group theory and generalizations (20-XX)
21 Quantum theory (81-XX)
18 Commutative algebra (13-XX)
18 Operator theory (47-XX)
17 Numerical analysis (65-XX)
16 Functions of a complex variable (30-XX)
16 Harmonic analysis on Euclidean spaces (42-XX)
15 Computer science (68-XX)
14 Probability theory and stochastic processes (60-XX)
13 Geometry (51-XX)
11 Dynamical systems and ergodic theory (37-XX)
10 Convex and discrete geometry (52-XX)
8 Associative rings and algebras (16-XX)
8 Approximations and expansions (41-XX)
7 Order, lattices, ordered algebraic structures (06-XX)
7 Manifolds and cell complexes (57-XX)
6 Statistics (62-XX)
5 History and biography (01-XX)
5 Nonassociative rings and algebras (17-XX)
5 \(K\)-theory (19-XX)
5 Ordinary differential equations (34-XX)
5 Partial differential equations (35-XX)
5 Statistical mechanics, structure of matter (82-XX)
4 General topology (54-XX)
4 Global analysis, analysis on manifolds (58-XX)
3 Category theory; homological algebra (18-XX)
3 Measure and integration (28-XX)
3 Mechanics of particles and systems (70-XX)
3 Operations research, mathematical programming (90-XX)
2 General and overarching topics; collections (00-XX)
2 Several complex variables and analytic spaces (32-XX)
2 Abstract harmonic analysis (43-XX)
2 Integral transforms, operational calculus (44-XX)
2 Mechanics of deformable solids (74-XX)
2 Fluid mechanics (76-XX)
1 Topological groups, Lie groups (22-XX)
1 Integral equations (45-XX)
1 Differential geometry (53-XX)
1 Optics, electromagnetic theory (78-XX)
1 Geophysics (86-XX)
1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
1 Systems theory; control (93-XX)
1 Mathematics education (97-XX)

Citations by Year