Gauss and Jacobi sums. Zbl 0906.11001
Berndt, Bruce C.; Evans, Ronald J.; Williams, Kenneth S. |
|
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. |
|
2002
|
Introductory algebraic number theory. Zbl 1035.11001
Alaca, Şaban; Williams, Kenneth S. |
|
2004
|
A simple norm inequality. Zbl 0178.16202
Dunkl, Charles F.; Williams, K. S. |
|
1964
|
Number theory in the spirit of Liouville. Zbl 1227.11002
Williams, Kenneth S. |
|
2011
|
Note on cubics over \(GF(2^n)\) and \(GF(3^n)\). Zbl 0321.12029
Williams, Kenneth S. |
|
1975
|
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. |
|
2007
|
Nineteen quaternary quadratic forms. Zbl 1131.11025
Alaca, Ayşe; Alaca, Şaban; Lemire, Mathieu F.; Williams, Kenneth S. |
|
2007
|
Integers of biquadratic fields. Zbl 0205.35401
Williams, Kenneth S. |
|
1970
|
The convolution sum \(\sum_{m<n/8} \sigma(m) \sigma(n-8m)\). Zbl 1130.11006
Williams, Kenneth S. |
|
2006
|
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. |
|
2007
|
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. |
|
2006
|
The convolution sum \(\sum_{m<n/16}\sigma(m)\sigma(n-16m)\). Zbl 1132.11305
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. |
|
2008
|
The convolution sum \(\sum_{m<n/9}\sigma(m)\sigma(n-9m)\). Zbl 1082.11003
Williams, Kenneth S. |
|
2005
|
The number of representations of a positive integer by certain octonary quadratic forms. Zbl 1213.11087
Alaca, Şaban; Williams, Kenneth S. |
|
2010
|
Evaluation of two convolution sums involving the sum of divisors function. Zbl 1163.11301
Lemire, Mathieu; Williams, Kenneth S. |
|
2006
|
On the two-dimensional theta functions of the Borweins. Zbl 1127.11035
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. |
|
2006
|
Some results on the generalized Stieltjes constants. Zbl 0808.11054
Zhang, Nanyue; Williams, Kenneth S. |
|
1994
|
Integral bases for quartic fields with quadratic subfields. Zbl 0826.11048
Huard, James G.; Spearman, Blair K.; Williams, Kenneth S. |
|
1995
|
On Tornheim’s double series. Zbl 0858.40008
Huard, James G.; Williams, Kenneth S.; Zhang, Nanyue |
|
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. |
|
2007
|
Quartics over GF(2\(^n\)). Zbl 0274.12013
Leonard, Philip A.; Williams, Kenneth S. |
|
1973
|
On the number of representations of \(n\) by \(ax^2+bxy+cy^2\). Zbl 1095.11024
Sun, Zhihong; Williams, Kenneth S. |
|
2006
|
Mertens’ theorem for arithmetic progressions. Zbl 0286.10022
Williams, Kenneth S. |
|
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. |
|
1987
|
Theta functions identities and representations by certain quaternary quadratic forms. Zbl 1163.11029
Alaca, Ayşe; Alaca, Şaban; Lemire, Mathieu F.; Williams, Kenneth S. |
|
2008
|
Fourier series of a class of eta quotients. Zbl 1252.11043
Williams, Kenneth S. |
|
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. |
|
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. |
|
2007
|
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. |
|
1995
|
Evaluation of some convolutions sums involving the sum of divisors functions. Zbl 1094.11004
Cheng, Nathalie; Williams, Kenneth S. |
|
2005
|
On
\[
\sum_{n=1}^ \infty (1/n^{2k})
\]. Zbl 0224.40008
Williams, Kenneth S. |
|
1971
|
Congruences for \(L\)-functions. Zbl 0972.11001
Urbanowicz, Jerzy; Williams, Kenneth S. |
|
2000
|
A restricted Epstein zeta function and the evaluation of some definite integrals. Zbl 1037.11023
Muzaffar, Habib; Williams, Kenneth S. |
|
2002
|
Special values of the Lerch zeta function and the evaluation of certain integrals. Zbl 0785.11046
Williams, Kenneth S.; Zhang, Nanyue |
|
1993
|
Some series representations of \(\zeta(2n+1)\). Zbl 0808.11053
Zhang, Nanyue; Williams, Kenneth S. |
|
1993
|
The \(n\)th power of a \(2\times 2\) matrix. Zbl 0789.15015
Williams, Kenneth S. |
|
1992
|
The integers of a cyclic quartic field. Zbl 0707.11078
Hudson, R. H.; Williams, K. S. |
|
1990
|
\(A_4\)-sextic fields with a power basis. Zbl 1229.11136
Eloff, Daniel; Spearman, Blair K.; Williams, Kenneth S. |
|
2007
|
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. |
|
1982
|
Fourteen octonary quadratic forms. Zbl 1228.11049
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. |
|
2010
|
Relative integral bases for quartic fields over quadratic subfields. Zbl 0853.11090
Spearman, B. K.; Williams, K. S. |
|
1996
|
Evaluation of two trigonometric sums. Zbl 0820.11010
Williams, Kenneth S.; Zhang, Nan-Yue |
|
1994
|
Binomial coefficients and Jacobi sums. Zbl 0551.12015
Hudson, Richard H.; Williams, Kenneth S. |
|
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. |
|
2008
|
The Chowla-Selberg formula for genera. Zbl 0855.11018
Huard, James G.; Kaplan, Pierre; Williams, Kenneth S. |
|
1995
|
Pascal’s triangle (mod 8). Zbl 0889.11007
Huard, James G.; Spearman, Blair K.; Williams, Kenneth S. |
|
1998
|
Evaluation of character sums connected with elliptic curves. Zbl 0369.10025
Williams, Kenneth S. |
|
1979
|
On the imaginary bicyclic biquadratic fields with class-number 2. Zbl 0379.12002
Buell, D. A.; Williams, H. C.; Williams, K. S. |
|
1977
|
The cyclotomic numbers of order seven. Zbl 0311.12008
Leonard, Philip A.; Williams, Kenneth S. |
|
1975
|
On the class number of \(Q(\sqrt{-p})\) modulo 16, for \(p\equiv 1\) (mod 8) a prime. Zbl 0393.12008
Williams, Kenneth S. |
|
1981
|
Some arithmetic identities involving divisor functions. Zbl 1318.11001
Alaca, Şaban; Uygul, Faruk; Williams, Kenneth S. |
|
2012
|
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. |
|
2007
|
Some Lambert series expansions of products of theta functions. Zbl 0938.11017
Williams, Kenneth S. |
|
1999
|
Note on Salie’s sum. Zbl 0224.10039
Williams, Kenneth S. |
|
1971
|
Pell’s equations \(X^ 2-mY^ 2=-1,-4\) and continued fractions. Zbl 0596.10013
Kaplan, Pierre; Williams, Kenneth S. |
|
1986
|
An Artin character and representations of primes by binary quadratic forms. II. Zbl 0485.12003
Halter-Koch, Franz; Kaplan, Pierre; Williams, Kenneth S. |
|
1982
|
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. |
|
1990
|
Determination of all imaginary cyclic quartic fields with class number 2. Zbl 0678.12003
Hardy, Kenneth; Hudson, Richard H.; Richman, David; Williams, Kenneth S. |
|
1989
|
Values of the Dedekind eta function at quadratic irrationalities. Zbl 0936.11026
van der Poorten, Alfred; Williams, Kenneth S. |
|
1999
|
Dihedral quintic fields with a power basis. Zbl 1161.11393
Lavallee, Melissa J.; Spearman, Blair K.; Williams, Kenneth S.; Yang, Qiduan |
|
2005
|
The simplest arithmetic proof of Jacobi’s four squares theorem. Zbl 0958.11029
Spearman, Blair K.; Williams, Kenneth S. |
|
2000
|
Convolution sums involving the divisor function. Zbl 1156.11301
Cheng, Nathalie; Williams, Kenneth S. |
|
2004
|
On Euler’s criterion for cubic nonresidues. Zbl 0273.10002
Williams, Kenneth S. |
|
1975
|
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. |
|
1982
|
Class numbers and biquadratic reciprocity. Zbl 0473.12004
Williams, Kenneth S.; Currie, James D. |
|
1982
|
Application of the Hurwitz zeta function to the evaluation of certain integrals. Zbl 0791.11045
Zhang, Nanyue; Williams, Kenneth S. |
|
1993
|
Seven octonary quadratic forms. Zbl 1171.11021
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. |
|
2008
|
On a double series of Chan and Ong. Zbl 1163.11318
Williams, Kenneth S. |
|
2006
|
The index of a cyclic quartic field. Zbl 1049.11111
Spearman, Blair K.; Williams, Kenneth S. |
|
2003
|
The distribution of solutions of congruences. Zbl 0158.29603
Chalk, John H. H.; Williams, K. S. |
|
1965
|
On exceptional polynomials. Zbl 0159.05304
Williams, K. S. |
|
1968
|
The septic character of \(2, 3, 5\) and \(7\). Zbl 0265.10004
Leonard, Philip A.; Williams, Kenneth S. |
|
1974
|
On two conjectures of Chowla. Zbl 0186.09301
Williams, Kenneth S. |
|
1969
|
Note on Dickson’s permutation polynomials. Zbl 0235.12011
Williams, Kenneth S. |
|
1971
|
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. |
|
1992
|
A rational octic reciprocity law. Zbl 0311.10004
Williams, Kenneth S. |
|
1976
|
The quadratic and quartic character of certain quadratic units. I. Zbl 0335.12006
Leonard, Philip A.; Williams, Kenneth S. |
|
1977
|
The quadratic and quartic character of certain quadratic units. II. Zbl 0386.12002
Leonard, Philip A.; Williams, Kenneth S. |
|
1979
|
Some new residuacity criteria. Zbl 0456.10001
Hudson, Richard H.; Williams, Kenneth S. |
|
1980
|
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. |
|
2008
|
The simplest \(D_4\)-octics. Zbl 1144.11074
Spearman, Blair K.; Williams, Kenneth S. |
|
2008
|
Values of the Euler phi function not divisible by a given odd prime. Zbl 1216.11089
Spearman, Blair K.; Williams, Kenneth S. |
|
2006
|
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. |
|
1986
|
Ramanujan identities and Euler products for a type of Dirichlet series. Zbl 1155.11026
Sun, Zhihong; Williams, Kenneth S. |
|
2006
|
Characterization of solvable quintics \(x^ 5+ ax+ b\). Zbl 0844.12002
Spearman, Blair K.; Williams, Kenneth S. |
|
1994
|
Cubic fields with index 2. Zbl 0992.11058
Spearman, Blair K.; Williams, Kenneth S. |
|
2002
|
An arithmetic proof of Jacobi’s eight squares theorem. Zbl 1004.11017
Williams, Kenneth S. |
|
2001
|
A Diophantine system of Dickson. Zbl 0299.12017
Leonard, Philip A.; Williams, Kenneth S. |
|
1974
|
The distribution of the residues of a quartic polynomial. Zbl 0171.00702
McCann, K.; Williams, K. S. |
|
1967
|
On the number of distinguished representations of a group element. Zbl 0248.20018
Jacobson, David; Williams, Kenneth S. |
|
1972
|
The cyclotomic numbers of order eleven. Zbl 0267.12009
Leonard, Philip A.; Williams, Kenneth S. |
|
1975
|
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. |
|
2014
|
A rational sixteenth power reciprocity law. Zbl 0363.10003
Leonard, Philip A.; Williams, Kenneth S. |
|
1977
|
On Scholz’s reciprocity law. Zbl 0372.12004
Williams, Kenneth S. |
|
1977
|
On the evaluation of the Legendre symbol \(((A+B\sqrt{m})/p)\). Zbl 0524.10002
Williams, Kenneth S.; Hardy, Kenneth; Friesen, Christian |
|
1985
|
Note on a result of Barrucand and Cohn. Zbl 0325.10002
Williams, Kenneth S. |
|
1976
|
A refinement of H. C. Williams’ \(q\)th root algorithm. Zbl 0782.11040
Williams, Kenneth S.; Hardy, Kenneth |
|
1993
|
\(p\)-integral bases of a quartic field defined by a trinomial \(x^4+ax+b\). Zbl 1050.11091
Alaca, Şaban; Williams, Kenneth S. |
|
2004
|
Lifting monogenic cubic fields to monogenic sextic fields. Zbl 1237.11045
Lavallee, Melisa J.; Spearman, Blair K.; Williams, Kenneth S. |
|
2011
|
Beyond the Basel problem. I. Zbl 1535.11122
Williams, Kenneth S. |
|
2023
|
An application of binary quadratic forms of discriminant \(-31\) to modular forms. Zbl 1501.11056
Aygin, Zafer Selcuk; Williams, Kenneth S. |
|
2022
|
Representation numbers of spinor regular ternary quadratic forms. Zbl 1506.11056
Aygin, Zafer Selcuk; Doyle, Greg; Münkel, Florian; Pehlivan, Lerna; Williams, Kenneth S. |
|
2021
|
Derivable quadratic forms and representation numbers. Zbl 1478.11056
Aygin, Zafer Selcuk; Williams, Kenneth S. |
|
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. |
|
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 |
|
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. |
|
2019
|
The many sides of the Pythagorean theorem. Zbl 1445.97011
Dlab, Vlastimil; Williams, Kenneth S. |
|
2019
|
\((k,l)\)-universality of ternary quadratic forms \(ax^2 + by^2 + cz^2\). Zbl 1450.11032
Pehlivan, Lerna; Williams, Kenneth S. |
|
2018
|
Evaluation of some \(q\)-integrals in terms of the Dedekind eta function. Zbl 1429.11079
Doyle, Greg; Williams, Kenneth S. |
|
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. |
|
2018
|
A positive-definite ternary quadratic form does not represent all positive integers. Zbl 1412.11065
Doyle, Greg; Williams, Kenneth S. |
|
2017
|
Some arithmetic convolution identities. Zbl 1422.11007
Williams, Kenneth S. |
|
2017
|
Infinite products with coefficients which vanish on certain arithmetic progressions. Zbl 1429.11078
Alaca, Ayşe; Alaca, Şaban; Aygin, Zafer Selcuk; Williams, Kenneth S. |
|
2017
|
A class of subsums of Euler’s sum. Zbl 1364.11009
Williams, Kenneth S. |
|
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. |
|
2016
|
Bounds for the representations of integers by positive quadratic forms. Zbl 1398.11068
Williams, Kenneth S. |
|
2016
|
A “four integers” theorem and a “five integers” theorem. Zbl 1327.11024
Williams, Kenneth S. |
|
2015
|
Historical remark on a theorem of Zhang and Yue. Zbl 1319.11076
Williams, Kenneth S. |
|
2015
|
Historical remark on Ramanujan’s tau function. Zbl 1336.11037
Williams, Kenneth S. |
|
2015
|
Ternary quadratic forms and eta quotients. Zbl 1336.11033
Williams, Kenneth S. |
|
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. |
|
2014
|
Double Gauss sums. Zbl 1366.11092
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. |
|
2014
|
Ternary quadratic forms \(ax^2+by^2+cz^2\) representing all positive integers \(8k+4\). Zbl 1327.11023
Williams, Kenneth S. |
|
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. |
|
2014
|
Quadratic forms and a product-to-sum formula. Zbl 1278.11043
Williams, Kenneth S. |
|
2013
|
The parents of Jacobi’s four squares theorem are unique. Zbl 1305.11026
Williams, Kenneth S. |
|
2013
|
Euler products in Ramanujan’s lost notebook. Zbl 1281.11086
Berndt, Bruce C.; Kim, Byungchan; Williams, Kenneth S. |
|
2013
|
Fourier series of a class of eta quotients. Zbl 1252.11043
Williams, Kenneth S. |
|
2012
|
Some arithmetic identities involving divisor functions. Zbl 1318.11001
Alaca, Şaban; Uygul, Faruk; Williams, Kenneth S. |
|
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. |
|
2012
|
Some product-to-sum identities. Zbl 1282.11039
Alaca, Şaban; Pehlivan, Lerna; Williams, Kenneth S. |
|
2012
|
Number theory in the spirit of Liouville. Zbl 1227.11002
Williams, Kenneth S. |
|
2011
|
Lifting monogenic cubic fields to monogenic sextic fields. Zbl 1237.11045
Lavallee, Melisa J.; Spearman, Blair K.; Williams, Kenneth S. |
|
2011
|
Restricted Eisenstein series and certain convolution sums. Zbl 1245.11095
Alaca, Ayşe; Alaca, Şaban; Uygul, Faruk; Williams, Kenneth S. |
|
2011
|
The number of representations of a positive integer by certain octonary quadratic forms. Zbl 1213.11087
Alaca, Şaban; Williams, Kenneth S. |
|
2010
|
Fourteen octonary quadratic forms. Zbl 1228.11049
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. |
|
2010
|
Sextenary quadratic forms and an identity of Klein and Fricke. Zbl 1228.11050
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. |
|
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. |
|
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. |
|
2009
|
Some new theta function identities with applications to sextenary quadratic forms. Zbl 1235.11039
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. |
|
2009
|
Sums of \(4k\) squares: a polynomial approach. Zbl 1239.11044
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. |
|
2009
|
Some infinite products of Ramanujan type. Zbl 1234.11141
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. |
|
2009
|
The convolution sum \(\sum_{m<n/16}\sigma(m)\sigma(n-16m)\). Zbl 1132.11305
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. |
|
2008
|
Theta functions identities and representations by certain quaternary quadratic forms. Zbl 1163.11029
Alaca, Ayşe; Alaca, Şaban; Lemire, Mathieu F.; Williams, Kenneth S. |
|
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. |
|
2008
|
Seven octonary quadratic forms. Zbl 1171.11021
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. |
|
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. |
|
2008
|
The simplest \(D_4\)-octics. Zbl 1144.11074
Spearman, Blair K.; Williams, Kenneth S. |
|
2008
|
On Liouville’s twelve squares theorem. Zbl 1242.11029
Williams, Kenneth S. |
|
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. |
|
2008
|
Indices of integers in cyclic cubic fields. Zbl 1247.11135
Spearman, B. K.; Williams, K. S. |
|
2008
|
Arithmetic progressions and binary quadratic forms. Zbl 1204.11073
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. |
|
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. |
|
2007
|
Nineteen quaternary quadratic forms. Zbl 1131.11025
Alaca, Ayşe; Alaca, Şaban; Lemire, Mathieu F.; Williams, Kenneth S. |
|
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. |
|
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. |
|
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. |
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2007
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\(A_4\)-sextic fields with a power basis. Zbl 1229.11136
Eloff, Daniel; Spearman, Blair K.; Williams, Kenneth S. |
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2007
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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. |
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2007
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Lambert series and Liouville’s identities. Zbl 1113.11004
Alaca, A.; Alaca, Ş.; McAfee, E.; Williams, K. S. |
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2007
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The simplest proof of Jacobi’s six squares theorem. Zbl 1204.11072
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. |
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2007
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An infinite class of identies. Zbl 1115.33017
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. |
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2007
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The convolution sum \(\sum_{m<n/8} \sigma(m) \sigma(n-8m)\). Zbl 1130.11006
Williams, Kenneth S. |
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2006
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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. |
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2006
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Evaluation of two convolution sums involving the sum of divisors function. Zbl 1163.11301
Lemire, Mathieu; Williams, Kenneth S. |
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2006
|
On the two-dimensional theta functions of the Borweins. Zbl 1127.11035
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. |
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2006
|
On the number of representations of \(n\) by \(ax^2+bxy+cy^2\). Zbl 1095.11024
Sun, Zhihong; Williams, Kenneth S. |
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2006
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On a double series of Chan and Ong. Zbl 1163.11318
Williams, Kenneth S. |
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2006
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Values of the Euler phi function not divisible by a given odd prime. Zbl 1216.11089
Spearman, Blair K.; Williams, Kenneth S. |
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2006
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Ramanujan identities and Euler products for a type of Dirichlet series. Zbl 1155.11026
Sun, Zhihong; Williams, Kenneth S. |
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2006
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\(\text{PSL}(2,5)\) sextic fields with a power basis. Zbl 1096.11038
Spearman, Blair K.; Watanabe, Aya; Williams, Kenneth S. |
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2006
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Cyclic cubic fields of given conductor and given index. Zbl 1104.11047
Silvester, Alan K.; Spearman, Blair K.; Williams, Kenneth S. |
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2006
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Evaluation of complete elliptic integrals of the first kind at singular moduli. Zbl 1139.11025
Muzaffar, Habib; Williams, Kenneth S. |
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2006
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Cyclic quartic fields with a unique normal integral basis. Zbl 1172.11038
Spearman, Blair K.; Williams, Kenneth S. |
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2006
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The prime ideal factorization of 2 in pure quartic fields with index 2. Zbl 1175.11061
Spearman, Blair K.; Williams, Kenneth S. |
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2006
|
The convolution sum \(\sum_{m<n/9}\sigma(m)\sigma(n-9m)\). Zbl 1082.11003
Williams, Kenneth S. |
|
2005
|
Evaluation of some convolutions sums involving the sum of divisors functions. Zbl 1094.11004
Cheng, Nathalie; Williams, Kenneth S. |
|
2005
|
Dihedral quintic fields with a power basis. Zbl 1161.11393
Lavallee, Melissa J.; Spearman, Blair K.; Williams, Kenneth S.; Yang, Qiduan |
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2005
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Irreducible quartic polynomials with factorization modulo \(p\). Zbl 1211.11037
Driver, Eric; Leonard, Philip A.; Williams, Kenneth S. |
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2005
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Watson’s method of solving a quintic equation. Zbl 1102.12001
Lavallee, Melisa J.; Spearman, Blair K.; Williams, Kenneth S. |
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2005
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Introductory algebraic number theory. Zbl 1035.11001
Alaca, Şaban; Williams, Kenneth S. |
|
2004
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Convolution sums involving the divisor function. Zbl 1156.11301
Cheng, Nathalie; Williams, Kenneth S. |
|
2004
|
\(p\)-integral bases of a quartic field defined by a trinomial \(x^4+ax+b\). Zbl 1050.11091
Alaca, Şaban; Williams, Kenneth S. |
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2004
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On the number of representations of a positive integer by a binary quadratic form. Zbl 1102.11024
Kaplan, Pierre; Williams, Kenneth S. |
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2004
|
Normal integral bases for Emma Lehmer’s parametric family of cyclic quintics. Zbl 1158.11343
Spearman, Blair K.; Williams, Kenneth S. |
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2004
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Evaluation of Weber’s functions at quadratic irrationalities. Zbl 1077.11031
Muzaffar, Habib; Williams, Kenneth S. |
|
2004
|
The factorization of 2 in cubic fields with index 2. Zbl 1080.11079
Alaca, Saban; Spearman, Blair K.; Williams, Kenneth S. |
|
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. |
|
2004
|
On Voronoi’s method for finding an integral basis of a cubic field. Zbl 1061.11056
Alaca, Şaban; Williams, Kenneth S. |
|
2004
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The index of a cyclic quartic field. Zbl 1049.11111
Spearman, Blair K.; Williams, Kenneth S. |
|
2003
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\(n=\Delta +\Delta +2(\Delta + \Delta)\). Zbl 1041.11022
Williams, Kenneth S. |
|
2003
|
The discriminant of a cyclic field of odd prime degree. Zbl 1074.11059
Spearman, Blair K.; Williams, Kenneth S. |
|
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. |
|
2003
|
Sums of twelve squares. Zbl 1023.11018
Huard, James G.; Williams, Kenneth S. |
|
2003
|
The index of a dihedral quartic field. Zbl 1049.11115
Silvester, Alan K.; Spearman, Blair K.; Williams, Kenneth S. |
|
2003
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Elementary evaluation of certain convolution sums involving divisor functions. Zbl 1062.11005
Huard, James G.; Ou, Zhiming M.; Spearman, Blair K.; Williams, Kenneth S. |
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2002
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A restricted Epstein zeta function and the evaluation of some definite integrals. Zbl 1037.11023
Muzaffar, Habib; Williams, Kenneth S. |
|
2002
|
Cubic fields with index 2. Zbl 0992.11058
Spearman, Blair K.; Williams, Kenneth S. |
|
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. |
|
2002
|
| ...and 167 more Documents |
