Dr. Saban Alaca
Professor, School of Mathematics and Statistics, Carleton University
Professor, School of Mathematics and Statistics, Carleton University
Character values of the Sidelnikov-Lempel-Cohn-Eastman sequences, Cryptogr. Commun. 8 (2016), 18 pp. (with G. Millar)
Explicit evaluation of double Gauss sums, J. Comb. Number Theory 8 (2016), Issue 3, 15 pp. (with G. Doyle)
Representations by certain octonary quadratic forms with coefficients 1, 2, 3 and 6, INTEGERS 15 (2015), Paper No. A5, 9 pp. (with Y. Kesicioglu)
On the number of representations of a positive integer as a sum of two binary quadratic forms, Int. J. Number Theory 10 (2014), 1395-1420. (with L. Pehlivan and K. S. Williams)
Some product-to-sum identities, Journal of Combinatorics and Number Theory 4 (2012), 35-52. (with L. Pehlivan and K. S. Williams)
Some arithmetic identities involving divisor functions, Functiones et Approximatio 46 (2012), 261--271. (with F. Uygul and K. S. Williams)
Restricted Eisenstein Series and Certain Convolution Sums, Journal of Combinatorics and Number Theory 3 (2011), 1-14. (with A. Alaca, F. Uygul, and K. S. Williams)
The number of representations of a positive integer by certain octonary quadratic forms, Functiones et Approximatio 43 (2010), 45-54. (with K. S. Williams)
Sextenary quadratic forms and an identity of Klein and Fricke, International Journal of Number Theory 6 (2010), 169-183. (with A. Alaca and K. S. Williams)
Fourteen octonary quadratic forms, International Journal of Number Theory 6 (2010), 37-50. (with A. Alaca and K. S. Williams)
Representations by sextenary quadratic forms whose coefficients are 1, 2 and 4, Acta Arithmetica 141 (2010), 289-309. (with A. Alaca, F. Uygul and K. S. Williams)
Sums of 4k squares: a polynomial approach, Journal of Combinatorics and Number Theory 1 (2009), 33-52. (with A. Alaca and K. S. Williams)
Some new theta function identities with applications to sextenary quadratic forms, Journal of Combinatorics and Number Theory 1 (2009), 89-98. (with A. Alaca and K. S. Williams)
Some infinite products of Ramanujan type, Canadian Mathematical Bulletin 52 (2009), 481-492. (with A. Alaca and K. S. Williams)
Evaluation of the sums \(\sum_{m\equiv a \hspace{-1mm} \pmod 4} \sigma(m) \sigma(n-m)\), Czechoslovak Mathematical Journal 59 (2009), 847-859. (with A. Alaca and K. S. Williams)
Some identities involving theta functions, Journal of Number Theory 129 (2009), 1404-1431. (with A. Alaca and K. S. Williams)
The number of representations of a positive integer by certain quaternary quadratic forms, International Journal of Number Theory 5 (2009), 13-40. (with A. Alaca, M. F. Lemire and K. S. Williams)
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 \(x^2 + 2y^2 + 2z^2 + 2t^2 + 2u^2 + 4v^2\), Far East Journal of Mathematical Sciences 30 (2008), 547-556.(with A. Alaca and K. S. Williams)
Seven octonary quadratic forms, Acta Arithmetica 135 (2008), 339-350. (with A. Alaca and K. S. Williams)
Berndt's curious formula, International Journal of Number Theory 4 (2008), 677-689.(with A. Alaca and K. S. Williams)
Theta function identities and representations by certain quaternary quadratic forms, Int. J. Number Theory 4 (2008), 219-239. (with A. Alaca, M. F. Lemire and K. S. Williams)
Theta function identities and representations by certain quaternary quadratic forms II, International Mathematical Forum 3 (2008), 539-579. (with A. Alaca, S. M. F. Lemire and K. S. Williams)
Arithmetic progressions and binary quadratic forms, American Mathematical Monthly 115 (2008), 252-254. (with A. Alaca and K. S. Williams)
The convolution sum \(\displaystyle \sum_{m \lt n/16} \hspace{-2mm} \sigma(m) \sigma(n-16m)\), Canadian Mathematical Bulletin 51 (2008), 3-14. (with A. Alaca and K. S. Williams)
Jacobi's identity and representation of integers by certain quaternary quadratic forms, Int. J. Modern Math. 2 (2007), 143-176. (with A. Alaca, M. F. Lemire and K. S. Williams)
On the quaternary forms \(x^2 + y^2 +z^2 + 5t^2\), \(x^2 + y^2 + 5z^2 + 5t^2\) and \(x^2 + 5y^2 + 5z^2 + 5t^2\), JP J. Algebra Number Theory Appl. 9 (2007), 37-53. (with A. Alaca and K. S. Williams)
The simplest proof of Jacobi's six squares theorem, Far East J. Math. Sci. 27 (2007), 187-192. (with A. Alaca and K. S. Williams)
Evaluation of the convolution sums \(\displaystyle \hspace{-2mm} \sum_{l+24m=n} \sigma(l) \sigma(m)\) and \(\displaystyle \sum_{3l+8m=n} \hspace{-2mm} \sigma(l) \sigma(m)\), Math. J. Okayama Univ. 49 (2007), 93-111. (with A. Alaca and K. S. Williams)
Nineteen quaternary quadratic forms, Acta Arithmetica 130 (2007), 277-310. (with A. Alaca, M. F. Lemire and K. S. Williams)
Evaluation of the convolution sums \(\displaystyle \sum_{l+ 6m =n} \hspace{-2mm} \sigma(l) \sigma(m)\) and \(\displaystyle \sum_{2l+ 3m =n} \hspace{-2mm} \sigma(l) \sigma(m)\), J. Number Theory 124 (2007), 491-510. (with K. S. Williams)
Lambert series and Liouville's identities, Dissertationes Math. 445 (2007), 1-72. (with A. Alaca, E. McAfee and K. S. Williams)
An infinite class of identities, Bull. Austral. Math. Soc. 75 (2007), 239-246. (with A. Alaca and K. S. Williams)
Nonexistence of a composition law, Math Mag. 80 (2007), 142-144. (with K. S. Williams)
Evaluation of the convolution sums \(\displaystyle \sum_{l+18m=n} \hspace{-2mm} \sigma(l)\sigma(m)\) and \(\displaystyle \sum_{2l+9m=n} \hspace{-2mm} \sigma(l)\sigma(m)\), International Mathematical Forum 2 (2007), 45-68. (with A. Alaca and K. S. Williams)
Congruences for Brewer sums, Finite Fields and Their Applications 13 (2007), 1-19.
Evaluation of the convolution sums \(\displaystyle \sum_{l+12m=n} \hspace{-2mm} \sigma(l)\sigma(m)\) and \(\displaystyle \sum_{3l+4m=n} \hspace{-2mm} \sigma(l)\sigma(m)\),
Advances in Theoretical and Applied Mathemeatics 1 (2006), 27-48. (with A. Alaca and K. S. Williams)
On the two-dimensional theta functions of the Borweins, Acta Arith. 124 (2006), 177-195.
(with A. Alaca and K. S. Williams)
Explicit decomposition of a rational prime in a cubic field, Int. J. Math. Math. Sci. 2006 (2006), 1-11. (with B. K. Spearman and K. S. Williams)
The factorization of 2 in cubic fields with index 2, Far East J. Math. Sci. 14 (2004), 273-282. (with K. S. Williams)
An integral basis and the discriminant of a quintic field defined by a trinomial x5 + ax + b, JP Journal of Algebra, Number Theory and Applications 4 (2004), 261-299, (with A. Alaca)
p-Integral bases of a quartic field defined by a trinomial x4 + ax + b, Far East J. Math. Sci. 12 (2004), 137-168. (with K. S. Williams)
On Voronoi's method for finding an integral basis of a cubic field, Util. Math. 65 (2004), 163-166. (with K. S. Williams)
A simple method for finding an integral basis of a quartic field defined by a trinomial x4+ax+b, JP J. Algebra Number Theory Appl. 3 (2003), 477-505. (with K. S. Williams)