Publications in Refereed Journals:
A. Alaca, Theta functions of nineteen non-diagonal positive-definite quaternary quadratic forms of discriminant \(784\) with levels \(28\) or \(56\). (Accepted for publication in Indian J. Pure Appl. Math. May 2022.)
G. Millar, M. Kulhandjian, A. Alaca, S. Alaca, C. D'Amours, H. Yanikomeroglu, Low-density spreading design based on an algebraic scheme for NOMA systems, IEEE Wireless Communications Letters 11 (2022), No. 4, 698-702.
A. Alaca, S. Alaca, K. S. Williams, Representation numbers of seven quaternary quadratic forms each in a genus consisting of only two classes, Turkish J. Math. 44 (2020), 1955-1981.
A. Alaca, S. Alaca, E. Ntienjem, The convolution sum \(\sum_{al+bm=n} \sigma(l) \sigma(m)\) for \((a,b)=(1,28), (4,7)\), \((1,14), (2,7), (1,7)\), Kyungpook Math. J., 59 (2019), No. 3, 377-389.
A. Alaca, M. Altiary, Representations by quaternary quadratic forms with coefficients \(1\), \(2\), \(5\) or \(10\), Commun. Korean Math. Soc., 34 (2019), No. 1, 27-41.
A. Alaca, S. Alaca, Z. S. Aygin, Eta quotients of level $12$ and weight \(1\), Turkish J. Math. 43 (2019), 1-8.
A. Alaca, S. Alaca, Z. S. Aygin, Eta quotients, Eisenstein series and Elliptic curves, INTEGERS 18 (2018), Paper No. A85, 12 pp.
A. Alaca, Representations by quaternary quadratic forms with coefficients \(1\), \(3\), \(5\) or \(15\), INTEGERS, 18 (2018), Paper No. A12, 14 pp.
A. Alaca, S. Alaca, Z. S. Aygin, K. S. Williams, Infinite products with coefficients which vanish on certain arithmetic progressions, Int. J. Number Theory, 13 (2017), 1095-1117.
A. Alaca, S. Alaca, Z. S. Aygin, Theta products and eta quotients of level \(24\) and weight \(2\), Funct. Approx. Comment. Math., 57 (2017), 205-234.
A. Alaca, M. N. Kesicioglu, Representations by octonary quadratic forms with coefficients \(1\), \(2\), \(3\) or \(6\), Int. J. Number Theory, 13 (2017), 735-749.
A. Alaca, J. Alanazi, Representations by quaternary quadratic forms with coefficients \(1\), \(2\), \(7\) or \(14\), INTEGERS 16 (2016), Paper No. A55, 16 pp.
A. Alaca, S. Alaca, K. S. Williams, Representation numbers of certain quaternary quadratic forms in a genus consisting of a single class, Int. J. Number Theory, 12 (2016), 1529-1573.
A. Alaca, S. Alaca, Z. S. Aygin, Fourier coefficients of a class of eta quotients of weight \(2\), Int. J. Number Theory, 11 (2015), 2381-2392.
A. Alaca, M. N. Kesicioglu, Representations by certain octonary quadratic forms with coefficients \(1\), \(3\) or \(9\), Int. J. Number Theory, 11 (2015), 2353-2368.
A. Alaca, S. Alaca, K. S. Williams, Double Gauss Sums, J. Comb. Number Theory 6 (2014), 127-153.
A. Alaca, Representations by certain octonary quadratic forms with coefficients \(1\), \(3\) or \(9\), Int. J. Number Theory 10 (2014), 1365-1384.
A. Alaca, K. S. Williams, 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 \(x^2 + 3y^2 + 6z^2 + 6t^2\), Int. J. Number Theory 8 (2012), 1661-1686.
A. Alaca, On the number of representations of a positive integer by certain quadratic forms in twelve variables, J. Comb. Number Theory 3 (2011), 167-177.
A. Alaca, Representations by quaternary quadratic forms whose coefficients are \(1, 4, 9\) and \(36\), J. Number Theory 131 (2011), 2192-2218.
A. Alaca, S. Alaca, F. Uygul, K. S. Williams, Restricted Eisenstein Series and Certain Convolution Sums, J. Comb. Number Theory 3 (2011), 1-14.
A. Alaca, S. Alaca, K. S. Williams, Sextenary quadratic forms and an identity of Klein and Fricke, Int. J. Number Theory 6 (2010), 169-183.
A. Alaca, S. Alaca, K. S. Williams, Fourteen octonary quadratic forms, Int. J. Number Theory 6 (2010), 37-50.
A. Alaca, S. Alaca, F. Uygul, K. S. Williams, Representations by sextenary quadratic forms whose coefficients are \(1,~2\) and \(4\), Acta Arith. 141 (2010), 289-309.
A. Alaca, S. Alaca, K. S. Williams, Sums of \(4k\) Squares: a Polynomial Approach, J. Comb. Number Theory 1 (2009), 133-152.
A. Alaca, S. Alaca, K. S. Williams, Some new theta function identities with applications to sextenary quadratic forms, J. Comb. Number Theory 1 (2009), 91-100.
A. Alaca, S. Alaca, K. S. Williams, Some infinite products of Ramanujan type, Canad. Math. Bull. 52 (2009), 481-492.
A. Alaca, S. Alaca, K. S. Williams, Evaluation of the sums \(\displaystyle \sum_{m\equiv a \! \pmod 4} \! \! \! \sigma(m) \sigma(n-m)\), Czechoslovak Math. J. 59 (2009), 847-859.
A. Alaca, S. Alaca, K. S. Williams, Some identities involving theta functions, J. Number Theory 129 (2009), 1404-1431.
A. Alaca, S. Alaca, M. F. Lemire, K. S. Williams, The number of representations of a positive integer by certain quaternary quadratic forms, Int. J. Number Theory 5 (2009), 13-40.
A. Alaca, Representations by quaternary quadratic forms whose coefficients are \(1, 3\) and \(9\), Acta Arith. 136 (2009), 151-166.
A. Alaca, S. Alaca, 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 J. Math. Sci. (FJMS) 30 (2008), 547-556.
A. Alaca, S. Alaca, K. S. Williams, Seven octonary quadratic forms, Acta Arith. 135 (2008), 439-350.
A. Alaca, S. Alaca, K. S. Williams, Berndt's curious formula, Int. J. Number Theory 4 (2008), 677-689.
A. Alaca, S. Alaca, M. F. Lemire, K. S. Williams, Theta function identities and representations by certain quaternary quadratic forms, Int. J. Number Theory 4 (2008), 219-239.
A. Alaca, S. Alaca, M. F. Lemire, K. S. Williams, Theta function identities and representations by certain quaternary quadratic forms II, Int. Math. Forum 3 (2008), 539-579.
A. Alaca, S. Alaca, K. S. Williams, Arithmetic progressions and binary quadratic forms, Amer. Math. Monthly 115 (2008), 252-254.
A. Alaca, S. Alaca, K. S. Williams, The convolution sum \(\displaystyle \sum_{m < n/16} \hspace{-3mm} \sigma(m) \sigma(n-16m)\), Canad. Math. Bull. 2 (2008), 3-14.
A. Alaca, S. Alaca, K. S. Williams, Jacobi's identity and the representation of integers by certain quaternary quadratic forms, Int. J. Mod. Math. 2 (2007), 143-176.
A. Alaca, S. Alaca, 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.
A. Alaca, S. Alaca, K. S. Williams, The simplest proof of Jacobi's six squares theorem, Far East J. Math. Sci. (FJMS) 27 (2007), 187-192.
A. Alaca, S. Alaca, K. S. Williams, Evaluation of the convolution sums \(\displaystyle \hspace{-2mm} \sum_{l+24m=n} \hspace{-4mm} \sigma(l) \sigma(m)\) and \(\displaystyle \sum_{3l+8m=n} \hspace{-4mm} \sigma(l) \sigma(m)\), Math. J. Okayama Univ. 49 (2007), 93-111.
A. Alaca, S. Alaca, M. F. Lemire and K. S. Williams, Nineteen quaternary quadratic forms, Acta Arith. 130 (2007), 277-310.
A. Alaca, S. Alaca, E. McAfee, K. S. Williams, Lambert series and Liouville's identities, Dissertationes Math. (Rozprawy Mat.) 445 (2007), 72 pp.
A. Alaca, S. Alaca, K. S. Williams, An infinite class of identities, Bull. Austral. Math. Soc. 75 (2007), 239-246.
A. Alaca, S. Alaca, K. S. Williams, Evaluation of the convolution sums \(\displaystyle \sum_{l+18m=n}\sigma(l)\sigma(m)\) and \(\displaystyle \sum_{2l+9m=n}\sigma(l)\sigma(m)\), Int. Math. Forum 2 (2007), 45-68.
A. Alaca, S. Alaca, K. S. Williams, Evaluation of the convolution sums \(\displaystyle \sum_{l+12m=n} \hspace{-4mm} \sigma(l)\sigma(m)\) and \(\displaystyle \sum_{3l+4m=n} \hspace{-4mm} \sigma(l)\sigma(m)\), Adv. Theor. Appl. Math. 1 (2006), 27-48.
A. Alaca, S. Alaca, K. S. Williams, On the two-dimensional theta functions of the Borweins, Acta Arith. 124 (2006), 177-195.
A. Alaca, S. Alaca, An integral basis and the discriminant of a quintic field defined by a trinomial \(x^{5}+ax+b\), JP J. Algebra Number Theory Appl. 4 (2004), 261-299.
Publication in Refereed Conference Proceedings:
A. Alaca, A. B. Mingarelli, An inverse matrix eigenvalue problem, Spectral Theory and Computational Methods of Sturm-Liouville Problems, 135--148, Lecture Notes in Pure and Appl. Math. 191, Dekker, 1997.
Edited Conference Proceedings:
A. Alaca, S. Alaca and K. S. Williams (Eds.), Advances in the Theory of Numbers, Fields Institute Communications, Proceedings of the Thirteenth Conference of the Canadian Number Theory Association, Springer, 2016.