Alaca, Ayşe Theta functions of nineteen non-diagonal positive-definite quaternary quadratic forms of discriminant 784 with levels 28 or 56. (English) Zbl 07706228 Indian J. Pure Appl. Math. 54, No. 2, 595-607 (2023). Reviewer: Nihal Özgür (İzmir) MSC: 11E20 11F27 11E25 11F11 11F20 11F30 PDFBibTeX XMLCite \textit{A. Alaca}, Indian J. Pure Appl. Math. 54, No. 2, 595--607 (2023; Zbl 07706228) Full Text: DOI
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth Representation numbers of seven quaternary quadratic forms each in a genus consisting of only two classes. (English) Zbl 1493.11080 Turk. J. Math. 44, No. 6, 1955-1981 (2020). MSC: 11E20 11E25 11F20 11F27 PDFBibTeX XMLCite \textit{A. Alaca} et al., Turk. J. Math. 44, No. 6, 1955--1981 (2020; Zbl 1493.11080) Full Text: DOI
Alaca, Ayşe; Alaca, Şaban; Ntienjem, Ebénézer The convolution sum \(\sum_{al+bm=n}\sigma(l)\sigma(m)\) for \((a,b) = (1,28),(4,7),(1,14),(2,7),(1,7)\). (English) Zbl 1455.11011 Kyungpook Math. J. 59, No. 3, 377-389 (2019). MSC: 11A25 11E20 11E25 11F11 11F20 PDFBibTeX XMLCite \textit{A. Alaca} et al., Kyungpook Math. J. 59, No. 3, 377--389 (2019; Zbl 1455.11011) Full Text: DOI arXiv
Alaca, Ayşe; Altiary, Mada Representations by quaternary quadratic forms with coefficients 1, 2, 5 or 10. (English) Zbl 1440.11048 Commun. Korean Math. Soc. 34, No. 1, 27-41 (2019). MSC: 11E25 11E20 11F11 11F20 11F27 PDFBibTeX XMLCite \textit{A. Alaca} and \textit{M. Altiary}, Commun. Korean Math. Soc. 34, No. 1, 27--41 (2019; Zbl 1440.11048) Full Text: DOI
Alaca, Ayşe; Alaca, Şaban; Aygin, Zafer Selçuk Eta quotients of level 12 and weight 1. (English) Zbl 1437.11057 Turk. J. Math. 43, No. 1, 1-8 (2019). MSC: 11F11 11F20 11F30 PDFBibTeX XMLCite \textit{A. Alaca} et al., Turk. J. Math. 43, No. 1, 1--8 (2019; Zbl 1437.11057) Full Text: DOI Link
Alaca, Ayşe; Alaca, Şaban; Aygin, Zafer Selcuk Eta quotients, Eisenstein series and elliptic curves. (English) Zbl 1440.11053 Integers 18, Paper A85, 12 p. (2018). MSC: 11F11 11F20 11G05 11Y35 PDFBibTeX XMLCite \textit{A. Alaca} et al., Integers 18, Paper A85, 12 p. (2018; Zbl 1440.11053) Full Text: arXiv Link
Alaca, Ayşe Representations by quaternary quadratic forms with coefficients 1, 3, 5, or 15. (English) Zbl 1446.11059 Integers 18, Paper A12, 14 p. (2018). MSC: 11E20 PDFBibTeX XMLCite \textit{A. Alaca}, Integers 18, Paper A12, 14 p. (2018; Zbl 1446.11059) Full Text: Link
Alaca, Ayşe; Alaca, Şaban; Aygin, Zafer Selcuk Theta products and eta quotients of level 24 and weight 2. (English) Zbl 1408.11026 Funct. Approximatio, Comment. Math. 57, No. 2, 205-234 (2017). MSC: 11F27 11F11 11F20 11F30 PDFBibTeX XMLCite \textit{A. Alaca} et al., Funct. Approximatio, Comment. Math. 57, No. 2, 205--234 (2017; Zbl 1408.11026) Full Text: DOI arXiv Euclid
Alaca, Ayşe; Kesicioğlu, M. Nesibe Representations by octonary quadratic forms with coefficients 1, 2, 3 or 6. (English) Zbl 1416.11053 Int. J. Number Theory 13, No. 3, 735-749 (2017). MSC: 11E25 11F11 11F20 11F27 11E20 PDFBibTeX XMLCite \textit{A. Alaca} and \textit{M. N. Kesicioğlu}, Int. J. Number Theory 13, No. 3, 735--749 (2017; Zbl 1416.11053) Full Text: DOI
Alaca, Ayşe; Alanazi, Jamilah Representations by quaternary quadratic forms with coefficients \(1, 2, 7\) or \(14\). (English) Zbl 1404.11036 Integers 16, Paper A55, 16 p. (2016). MSC: 11E20 11E25 11F11 PDFBibTeX XMLCite \textit{A. Alaca} and \textit{J. Alanazi}, Integers 16, Paper A55, 16 p. (2016; Zbl 1404.11036) Full Text: EMIS
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. Representation numbers of certain quaternary quadratic forms in a genus consisting of a single class. (English) Zbl 1350.11050 Int. J. Number Theory 12, No. 6, 1529-1573 (2016). Reviewer: Anton Shutov (Vladimir) MSC: 11E20 11E25 11L05 PDFBibTeX XMLCite \textit{A. Alaca} et al., Int. J. Number Theory 12, No. 6, 1529--1573 (2016; Zbl 1350.11050) Full Text: DOI
Alaca, Ayşe; Altiary, Mada Representations by Quaternary Quadratic Forms with Coefficients \(1\), \(2\), \(5\) or \(10\). arXiv:1607.03196 Preprint, arXiv:1607.03196 [math.NT] (2016). MSC: 11E25 11E20 11F11 11F20 11F27 BibTeX Cite \textit{A. Alaca} and \textit{M. Altiary}, ``Representations by Quaternary Quadratic Forms with Coefficients $1$, $2$, $5$ or $10$'', Preprint, arXiv:1607.03196 [math.NT] (2016) Full Text: arXiv OA License
Alaca, Ayşe; Alaca, Şaban; Ntienjem, Ebénézer Evaluation of the Convolution Sum involving the Sum of Divisors Function for 14, 22 and 26. arXiv:1604.02329 Preprint, arXiv:1604.02329 [math.NT] (2016). MSC: 11A25 11E20 11E25 11F11 11F20 11F27 BibTeX Cite \textit{A. Alaca} et al., ``Evaluation of the Convolution Sum involving the Sum of Divisors Function for 14, 22 and 26'', Preprint, arXiv:1604.02329 [math.NT] (2016) Full Text: arXiv OA License
Alaca, Ayse; Alaca, Saban; Aygin, Zafer Selcuk A family of Eta Quotients and an Extension of the Ramanujan-Mordell Theorem. arXiv:1603.09412 Preprint, arXiv:1603.09412 [math.NT] (2016). MSC: 11F11 11F20 11F27 11E20 11E25 11F30 11Y35 BibTeX Cite \textit{A. Alaca} et al., ``A family of Eta Quotients and an Extension of the Ramanujan-Mordell Theorem'', Preprint, arXiv:1603.09412 [math.NT] (2016) Full Text: arXiv OA License
Alaca, Ayşe; Alaca, Şaban; Aygin, Zafer Selçuk Fourier coefficients of a class of eta quotients of weight 2. (English) Zbl 1337.11025 Int. J. Number Theory 11, No. 8, 2381-2392 (2015). Reviewer: Kaori Ota (Tokyo) MSC: 11F11 11F20 11F30 11E20 PDFBibTeX XMLCite \textit{A. Alaca} et al., Int. J. Number Theory 11, No. 8, 2381--2392 (2015; Zbl 1337.11025) Full Text: DOI
Alaca, Ayşe; Kesicioğlu, M. Nesibe Representations by octonary quadratic forms with coefficients 1, 3 or 9. (English) Zbl 1341.11015 Int. J. Number Theory 11, No. 8, 2353-2368 (2015). Reviewer: Andrew G. Earnest (Carbondale) MSC: 11E25 11F11 11F20 PDFBibTeX XMLCite \textit{A. Alaca} and \textit{M. N. Kesicioğlu}, Int. J. Number Theory 11, No. 8, 2353--2368 (2015; Zbl 1341.11015) Full Text: DOI arXiv
Alaca, Ayşe (ed.); Alaca, Şaban (ed.); Williams, Kenneth S. (ed.) Advances in the theory of numbers. Proceedings of the thirteenth conference of the Canadian Number Theory Association, CNTA, Ottawa, Canada, June 16–20, 2014. (English) Zbl 1333.11004 Fields Institute Communications 77. Toronto: The Fields Institute for Research in the Mathematical Sciences; New York, NY: Springer (ISBN 978-1-4939-3200-9/hbk; 978-1-4939-3201-6/ebook). xx, 235 p. (2015). MSC: 11-06 11A25 11E81 11M06 11A41 11B25 11B39 11G05 11E12 14J20 14G20 00B25 PDFBibTeX XMLCite \textit{A. Alaca} (ed.) et al., Advances in the theory of numbers. Proceedings of the thirteenth conference of the Canadian Number Theory Association, CNTA, Ottawa, Canada, June 16--20, 2014. Toronto: The Fields Institute for Research in the Mathematical Sciences; New York, NY: Springer (2015; Zbl 1333.11004) Full Text: DOI
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. Double Gauss sums. (English) Zbl 1366.11092 J. Comb. Number Theory 6, No. 2, 127-153 (2014). MSC: 11L03 11L05 11T23 11E16 11E25 11D79 PDFBibTeX XMLCite \textit{A. Alaca} et al., J. Comb. Number Theory 6, No. 2, 127--153 (2014; Zbl 1366.11092) Full Text: Link
Alaca, Ayşe Representations by certain octonary quadratic forms with coefficients 1, 3 or 9. (English) Zbl 1301.11043 Int. J. Number Theory 10, No. 6, 1365-1384 (2014). Reviewer: Meinhard Peters (Münster) MSC: 11E25 11E20 11F11 11F20 11F27 PDFBibTeX XMLCite \textit{A. Alaca}, Int. J. Number Theory 10, No. 6, 1365--1384 (2014; Zbl 1301.11043) Full Text: DOI
Alaca, Ayşe; Williams, Kenneth S. 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 \(2x^2+3y^2+6z^2+6t^2\). (English) Zbl 1255.11020 Int. J. Number Theory 8, No. 7, 1661-1686 (2012). MSC: 11E20 11E25 11F27 PDFBibTeX XMLCite \textit{A. Alaca} and \textit{K. S. Williams}, Int. J. Number Theory 8, No. 7, 1661--1686 (2012; Zbl 1255.11020) Full Text: DOI
Alaca, Ayşe On the number of representations of a positive integer by certain quadratic forms in twelve variables. (English) Zbl 1282.11018 J. Comb. Number Theory 3, No. 3, 167-177 (2011). MSC: 11E25 11F27 PDFBibTeX XMLCite \textit{A. Alaca}, J. Comb. Number Theory 3, No. 3, 167--177 (2011; Zbl 1282.11018)
Alaca, Ayşe Representations by quaternary quadratic forms whose coefficients are 1, 4, 9 and 36. (English) Zbl 1248.11028 J. Number Theory 131, No. 11, 2192-2218 (2011). Reviewer: Ahmet Tekcan (Bursa) MSC: 11E25 11E20 PDFBibTeX XMLCite \textit{A. Alaca}, J. Number Theory 131, No. 11, 2192--2218 (2011; Zbl 1248.11028) Full Text: DOI
Alaca, Ayşe; Alaca, Şaban; Uygul, Faruk; Williams, Kenneth S. Representations by sextenary quadratic forms whose coefficients are 1, 2 and 4. (English) Zbl 1213.11085 Acta Arith. 141, No. 3, 289-309 (2010). Reviewer: Ahmet Tekcan (Bursa) MSC: 11E25 PDFBibTeX XMLCite \textit{A. Alaca} et al., Acta Arith. 141, No. 3, 289--309 (2010; Zbl 1213.11085) Full Text: DOI
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. Sextenary quadratic forms and an identity of Klein and Fricke. (English) Zbl 1228.11050 Int. J. Number Theory 6, No. 1, 169-183 (2010). MSC: 11E25 PDFBibTeX XMLCite \textit{A. Alaca} et al., Int. J. Number Theory 6, No. 1, 169--183 (2010; Zbl 1228.11050) Full Text: DOI
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. Fourteen octonary quadratic forms. (English) Zbl 1228.11049 Int. J. Number Theory 6, No. 1, 37-50 (2010). MSC: 11E25 11A25 PDFBibTeX XMLCite \textit{A. Alaca} et al., Int. J. Number Theory 6, No. 1, 37--50 (2010; Zbl 1228.11049) Full Text: DOI
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. Sums of \(4k\) squares: a polynomial approach. (English) Zbl 1239.11044 J. Comb. Number Theory 1, No. 2, 133-152 (2009). Reviewer: Meinhard Peters (Münster) MSC: 11E25 PDFBibTeX XMLCite \textit{A. Alaca} et al., J. Comb. Number Theory 1, No. 2, 133--152 (2009; Zbl 1239.11044)
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. Some new theta function identities with applications to sextenary quadratic forms. (English) Zbl 1235.11039 J. Comb. Number Theory 1, No. 1, 91-100 (2009). MSC: 11E25 PDFBibTeX XMLCite \textit{A. Alaca} et al., J. Comb. Number Theory 1, No. 1, 91--100 (2009; Zbl 1235.11039)
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. Some infinite products of Ramanujan type. (English) Zbl 1234.11141 Can. Math. Bull. 52, No. 4, 481-492 (2009). MSC: 11P84 11E25 11F11 11F27 33E05 PDFBibTeX XMLCite \textit{A. Alaca} et al., Can. Math. Bull. 52, No. 4, 481--492 (2009; Zbl 1234.11141) Full Text: DOI
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. Some identities involving theta functions. (English) Zbl 1173.11027 J. Number Theory 129, No. 6, 1404-1431 (2009). Reviewer: Florin Nicolae (Berlin) MSC: 11F27 11E25 11B68 PDFBibTeX XMLCite \textit{A. Alaca} et al., J. Number Theory 129, No. 6, 1404--1431 (2009; Zbl 1173.11027) Full Text: DOI
Alaca, Ayşe; Alaca, Şaban; Lemire, Mathieu F.; Williams, Kenneth S. The number of representations of a positive integer by certain quaternary quadratic forms. (English) Zbl 1221.11097 Int. J. Number Theory 5, No. 1, 13-40 (2009). Reviewer: Andrew G. Earnest (Carbondale) MSC: 11E25 11E20 11E12 PDFBibTeX XMLCite \textit{A. Alaca} et al., Int. J. Number Theory 5, No. 1, 13--40 (2009; Zbl 1221.11097) Full Text: DOI
Alaca, Ayşe Representations by quaternary quadratic forms whose coefficients are \(1,3\) and \(9\). (English) Zbl 1234.11045 Acta Arith. 136, No. 2, 151-166 (2009). Reviewer: Ahmet Tekcan (Bursa) MSC: 11E25 11E20 PDFBibTeX XMLCite \textit{A. Alaca}, Acta Arith. 136, No. 2, 151--166 (2009; Zbl 1234.11045) Full Text: DOI
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. Arithmetic progressions and binary quadratic forms. (English) Zbl 1204.11073 Am. Math. Mon. 115, No. 3, 252-254 (2008). Reviewer: Olaf Ninnemann (Berlin) MSC: 11E25 11E12 PDFBibTeX XMLCite \textit{A. Alaca} et al., Am. Math. Mon. 115, No. 3, 252--254 (2008; Zbl 1204.11073) Full Text: DOI
Alaca, Ayşe; Alaca, Şaban; Lemire, Mathieu F.; Williams, Kenneth S. Theta functions identities and representations by certain quaternary quadratic forms. (English) Zbl 1163.11029 Int. J. Number Theory 4, No. 2, 219-239 (2008). Reviewer: Andrew G. Earnest (Carbondale) MSC: 11E25 11E20 11D45 PDFBibTeX XMLCite \textit{A. Alaca} et al., Int. J. Number Theory 4, No. 2, 219--239 (2008; Zbl 1163.11029) Full Text: DOI
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. 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 \(x^2 +2y^2+2z^2+2t^2+2u^2+4v^2\). (English) Zbl 1213.11086 Far East J. Math. Sci. (FJMS) 30, No. 3, 547-556 (2008). MSC: 11E25 PDFBibTeX XMLCite \textit{A. Alaca} et al., Far East J. Math. Sci. (FJMS) 30, No. 3, 547--556 (2008; Zbl 1213.11086) Full Text: Link
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. Seven octonary quadratic forms. (English) Zbl 1171.11021 Acta Arith. 135, No. 4, 339-350 (2008). Reviewer: Scott D. Kominers (Cambridge, MA) MSC: 11E25 11A25 PDFBibTeX XMLCite \textit{A. Alaca} et al., Acta Arith. 135, No. 4, 339--350 (2008; Zbl 1171.11021) Full Text: DOI
Alaca, Ayşe; Alaca, Şaban; Lemire, Mathieu F.; Williams, Kenneth S. Theta function identities and representations by certain quaternary quadratic forms. II. (English) Zbl 1209.11041 Int. Math. Forum 3, No. 9-12, 539-579 (2008). Reviewer: Florin Nicolae (Berlin) MSC: 11E20 11E25 PDFBibTeX XMLCite \textit{A. Alaca} et al., Int. Math. Forum 3, No. 9--12, 539--579 (2008; Zbl 1209.11041)
Alaca, Ayşe; Alaca, Şaban; Wiliams, Kenneth S. Berndt’s curious formula. (English) Zbl 1166.11005 Int. J. Number Theory 4, No. 4, 677-689 (2008). MSC: 11A25 11E20 11E25 PDFBibTeX XMLCite \textit{A. Alaca} et al., Int. J. Number Theory 4, No. 4, 677--689 (2008; Zbl 1166.11005) Full Text: DOI
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. The convolution sum \(\sum_{m<n/16}\sigma(m)\sigma(n-16m)\). (English) Zbl 1132.11305 Can. Math. Bull. 51, No. 1, 3-14 (2008). MSC: 11A25 11E20 11E25 PDFBibTeX XMLCite \textit{A. Alaca} et al., Can. Math. Bull. 51, No. 1, 3--14 (2008; Zbl 1132.11305) Full Text: DOI
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. Evaluation of the convolution sums \(\sum_{l+18m=n}\sigma(l)\sigma(m)\) and \(\sum_{2l+9m=n}\sigma(l)\sigma(m)\). (English) Zbl 1163.11003 Int. Math. Forum 2, No. 1-4, 45-68 (2007). Reviewer: Scott D. Kominers (Cambridge, MA) MSC: 11A25 11E25 11E20 11F11 PDFBibTeX XMLCite \textit{A. Alaca} et al., Int. Math. Forum 2, No. 1--4, 45--68 (2007; Zbl 1163.11003) Full Text: DOI
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. On the quaternary forms \(x^2+y^2+z^2+5t^2\), \(x^2+y^2+5z^2+5t^2\) and \(x^2+5y^2+5z^2+5t^2\). (English) Zbl 1196.11058 JP J. Algebra Number Theory Appl. 9, No. 1, 37-53 (2007). MSC: 11E25 11E20 PDFBibTeX XMLCite \textit{A. Alaca} et al., JP J. Algebra Number Theory Appl. 9, No. 1, 37--53 (2007; Zbl 1196.11058) Full Text: Link
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. The simplest proof of Jacobi’s six squares theorem. (English) Zbl 1204.11072 Far East J. Math. Sci. (FJMS) 27, No. 1, 187-192 (2007). Reviewer: Florin Nicolae (Berlin) MSC: 11E25 11F27 PDFBibTeX XMLCite \textit{A. Alaca} et al., Far East J. Math. Sci. (FJMS) 27, No. 1, 187--192 (2007; Zbl 1204.11072)
Alaca, Ayşe; Alaca, Şaban; Lemire, Mathieu F.; Williams, Kenneth S. Jacobi’s identity and representations of integers by certain quaternary quadratic forms. (English) Zbl 1209.11040 Int. J. Mod. Math. 2, No. 2, 143-176 (2007). Reviewer: Olaf Ninnemann (Berlin) MSC: 11E20 11E25 11F27 PDFBibTeX XMLCite \textit{A. Alaca} et al., Int. J. Mod. Math. 2, No. 2, 143--176 (2007; Zbl 1209.11040)
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. Evaluation of the convolution sums \(\sum_{l+24m=n}\sigma(l)\sigma(m)\) and \(\sum_{3l+8m=n}\sigma(l)\sigma(m)\). (English) Zbl 1132.11304 Math. J. Okayama Univ. 49, 93-111 (2007). MSC: 11A25 11E20 11E25 PDFBibTeX XMLCite \textit{A. Alaca} et al., Math. J. Okayama Univ. 49, 93--111 (2007; Zbl 1132.11304)
Alaca, Ayşe; Alaca, Şaban; Lemire, Mathieu F.; Williams, Kenneth S. Nineteen quaternary quadratic forms. (English) Zbl 1131.11025 Acta Arith. 130, No. 3, 277-310 (2007). Reviewer: Meinhard Peters (Münster) MSC: 11E20 11E25 PDFBibTeX XMLCite \textit{A. Alaca} et al., Acta Arith. 130, No. 3, 277--310 (2007; Zbl 1131.11025) Full Text: DOI
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. An infinite class of identies. (English) Zbl 1115.33017 Bull. Aust. Math. Soc. 75, No. 2, 239-246 (2007). Reviewer: Gabriele Nebe (Aachen) MSC: 33E05 11F11 PDFBibTeX XMLCite \textit{A. Alaca} et al., Bull. Aust. Math. Soc. 75, No. 2, 239--246 (2007; Zbl 1115.33017) Full Text: DOI
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. Evaluation of the convolution sums \(\sum_{l+12m=n}\sigma(l)\sigma(m)\) and \(\sum_{3l+4m=n}\sigma(l)\sigma(m)\). (English) Zbl 1154.11003 Adv. Theor. Appl. Math. 1, No. 1, 27-48 (2006). Reviewer: Scott D. Kominers (Cambridge, MA) MSC: 11A25 11E25 11E20 PDFBibTeX XMLCite \textit{A. Alaca} et al., Adv. Theor. Appl. Math. 1, No. 1, 27--48 (2006; Zbl 1154.11003)
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S. On the two-dimensional theta functions of the Borweins. (English) Zbl 1127.11035 Acta Arith. 124, No. 2, 177-195 (2006). Reviewer: Florin Nicolae (Berlin) MSC: 11F27 11E20 11E25 11D45 PDFBibTeX XMLCite \textit{A. Alaca} et al., Acta Arith. 124, No. 2, 177--195 (2006; Zbl 1127.11035) Full Text: DOI