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Alaca, Şaban

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Author ID: alaca.saban Recent zbMATH articles by "Alaca, Şaban"
Published as: Alaca, Şaban; Alaca, Saban; Alaca, Ş.
Documents Indexed: 61 Publications since 1998, including 2 Books

Publications by Year

Citations contained in zbMATH Open

47 Publications have been cited 373 times in 151 Documents Cited by Year
Introductory algebraic number theory. Zbl 1035.11001
Alaca, Şaban; Williams, Kenneth S.
35
2004
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.
33
2007
Nineteen quaternary quadratic forms. Zbl 1131.11025
Alaca, Ayşe; Alaca, Şaban; Lemire, Mathieu F.; Williams, Kenneth S.
30
2007
The convolution sum \(\sum_{m<n/16}\sigma(m)\sigma(n-16m)\). Zbl 1132.11305
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
25
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.
24
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.
23
2006
The number of representations of a positive integer by certain octonary quadratic forms. Zbl 1213.11087
Alaca, Şaban; Williams, Kenneth S.
23
2010
On the two-dimensional theta functions of the Borweins. Zbl 1127.11035
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
22
2006
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.
17
2007
Theta functions identities and representations by certain quaternary quadratic forms. Zbl 1163.11029
Alaca, Ayşe; Alaca, Şaban; Lemire, Mathieu F.; Williams, Kenneth S.
17
2008
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.
12
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.
10
2007
Fourteen octonary quadratic forms. Zbl 1228.11049
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
9
2010
Evaluation of the convolution sums \(\sum_{l+27m=n}{\sigma}(l){\sigma}(m)\) and \(\sum_{l+32m=n}{\sigma}(l){\sigma}(m)\). Zbl 1360.11010
Alaca, Şaban; Kesicioğlu, Yavuz
8
2016
Theta function identities and representations by certain quaternary quadratic forms. II. Zbl 1209.11041
Alaca, Ayşe; Alaca, Şaban; Lemire, Mathieu F.; Williams, Kenneth S.
7
2008
Some arithmetic identities involving divisor functions. Zbl 1318.11001
Alaca, Şaban; Uygul, Faruk; Williams, Kenneth S.
7
2012
Fourier coefficients of a class of eta quotients of weight 2. Zbl 1337.11025
Alaca, Ayşe; Alaca, Şaban; Aygin, Zafer Selçuk
6
2015
Seven octonary quadratic forms. Zbl 1171.11021
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
6
2008
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.
5
2007
\(p\)-integral bases of a cubic field. Zbl 0908.11048
Alaca, Saban
4
1998
Congruences for Brewer sums. Zbl 1107.11032
Alaca, Şaban
4
2007
Some new theta function identities with applications to sextenary quadratic forms. Zbl 1235.11039
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
4
2009
Representations by certain octonary quadratic forms whose coefficients are \(1, 2, 3\) and \(6\). Zbl 1283.11066
Alaca, Şaban; Kesicioğlu, Yavuz
4
2014
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
Lambert series and Liouville’s identities. Zbl 1113.11004
Alaca, A.; Alaca, Ş.; McAfee, E.; Williams, K. S.
3
2007
Sextenary quadratic forms and an identity of Klein and Fricke. Zbl 1228.11050
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
3
2010
Some infinite products of Ramanujan type. Zbl 1234.11141
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
3
2009
Representations by certain octonary quadratic forms with coefficients \(1, 2, 3,\) and \(6\). Zbl 1352.11041
Alaca, Şaban; Kesicioğlu, Yavuz
2
2015
Theta products and eta quotients of level 24 and weight 2. Zbl 1408.11026
Alaca, Ayşe; Alaca, Şaban; Aygin, Zafer Selcuk
2
2017
\(p\)-integral bases of algebraic number fields. Zbl 0999.11063
Alaca, Şaban
2
1999
Sums of \(4k\) squares: a polynomial approach. Zbl 1239.11044
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
2
2009
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
Restricted Eisenstein series and certain convolution sums. Zbl 1245.11095
Alaca, Ayşe; Alaca, Şaban; Uygul, Faruk; Williams, Kenneth S.
2
2011
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.
1
2014
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
Double Gauss sums. Zbl 1366.11092
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
1
2014
Infinite products with coefficients which vanish on certain arithmetic progressions. Zbl 1429.11078
Alaca, Ayşe; Alaca, Şaban; Aygin, Zafer Selcuk; Williams, Kenneth S.
1
2017
\(p\)-integral bases of a quartic field defined by a trinomial \(x^4+ax+b\). Zbl 1050.11091
Alaca, Şaban; Williams, Kenneth S.
1
2004
On Voronoi’s method for finding an integral basis of a cubic field. Zbl 1061.11056
Alaca, Şaban; 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 simplest proof of Jacobi’s six squares theorem. Zbl 1204.11072
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
1
2007
Arithmetic progressions and binary quadratic forms. Zbl 1204.11073
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
1
2008
An infinite class of identies. Zbl 1115.33017
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
1
2007
Some product-to-sum identities. Zbl 1282.11039
Alaca, Şaban; Pehlivan, Lerna; Williams, Kenneth S.
1
2012
Character values of the Sidelnikov-Lempel-Cohn-Eastman sequences. Zbl 1369.94508
Alaca, Şaban; Millar, Goldwyn
1
2017
The convolution sum \(\sum_{al+bm=n}\sigma(l)\sigma(m)\) for \((a,b) = (1,28),(4,7),(1,14),(2,7),(1,7)\). Zbl 1455.11011
Alaca, Ayşe; Alaca, Şaban; Ntienjem, Ebénézer
1
2019
Eta quotients of level 12 and weight 1. Zbl 1437.11057
Alaca, Ayşe; Alaca, Şaban; Aygin, Zafer Selçuk
1
2019
The convolution sum \(\sum_{al+bm=n}\sigma(l)\sigma(m)\) for \((a,b) = (1,28),(4,7),(1,14),(2,7),(1,7)\). Zbl 1455.11011
Alaca, Ayşe; Alaca, Şaban; Ntienjem, Ebénézer
1
2019
Eta quotients of level 12 and weight 1. Zbl 1437.11057
Alaca, Ayşe; Alaca, Şaban; Aygin, Zafer Selçuk
1
2019
Theta products and eta quotients of level 24 and weight 2. Zbl 1408.11026
Alaca, Ayşe; Alaca, Şaban; Aygin, Zafer Selcuk
2
2017
Infinite products with coefficients which vanish on certain arithmetic progressions. Zbl 1429.11078
Alaca, Ayşe; Alaca, Şaban; Aygin, Zafer Selcuk; Williams, Kenneth S.
1
2017
Character values of the Sidelnikov-Lempel-Cohn-Eastman sequences. Zbl 1369.94508
Alaca, Şaban; Millar, Goldwyn
1
2017
Evaluation of the convolution sums \(\sum_{l+27m=n}{\sigma}(l){\sigma}(m)\) and \(\sum_{l+32m=n}{\sigma}(l){\sigma}(m)\). Zbl 1360.11010
Alaca, Şaban; Kesicioğlu, Yavuz
8
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
Fourier coefficients of a class of eta quotients of weight 2. Zbl 1337.11025
Alaca, Ayşe; Alaca, Şaban; Aygin, Zafer Selçuk
6
2015
Representations by certain octonary quadratic forms with coefficients \(1, 2, 3,\) and \(6\). Zbl 1352.11041
Alaca, Şaban; Kesicioğlu, Yavuz
2
2015
Representations by certain octonary quadratic forms whose coefficients are \(1, 2, 3\) and \(6\). Zbl 1283.11066
Alaca, Şaban; Kesicioğlu, Yavuz
4
2014
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.
1
2014
Double Gauss sums. Zbl 1366.11092
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
1
2014
Some arithmetic identities involving divisor functions. Zbl 1318.11001
Alaca, Şaban; Uygul, Faruk; Williams, Kenneth S.
7
2012
Some product-to-sum identities. Zbl 1282.11039
Alaca, Şaban; Pehlivan, Lerna; Williams, Kenneth S.
1
2012
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.
23
2010
Fourteen octonary quadratic forms. Zbl 1228.11049
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
9
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.
12
2009
Some new theta function identities with applications to sextenary quadratic forms. Zbl 1235.11039
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
4
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.
2
2009
The convolution sum \(\sum_{m<n/16}\sigma(m)\sigma(n-16m)\). Zbl 1132.11305
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
25
2008
Theta functions identities and representations by certain quaternary quadratic forms. Zbl 1163.11029
Alaca, Ayşe; Alaca, Şaban; Lemire, Mathieu F.; Williams, Kenneth S.
17
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.
7
2008
Seven octonary quadratic forms. Zbl 1171.11021
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
6
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
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.
33
2007
Nineteen quaternary quadratic forms. Zbl 1131.11025
Alaca, Ayşe; Alaca, Şaban; Lemire, Mathieu F.; Williams, Kenneth S.
30
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.
24
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.
17
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.
10
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.
5
2007
Congruences for Brewer sums. Zbl 1107.11032
Alaca, Şaban
4
2007
Lambert series and Liouville’s identities. Zbl 1113.11004
Alaca, A.; Alaca, Ş.; McAfee, E.; Williams, K. S.
3
2007
The simplest proof of Jacobi’s six squares theorem. Zbl 1204.11072
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
1
2007
An infinite class of identies. Zbl 1115.33017
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
1
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.
23
2006
On the two-dimensional theta functions of the Borweins. Zbl 1127.11035
Alaca, Ayşe; Alaca, Şaban; Williams, Kenneth S.
22
2006
Introductory algebraic number theory. Zbl 1035.11001
Alaca, Şaban; Williams, Kenneth S.
35
2004
\(p\)-integral bases of a quartic field defined by a trinomial \(x^4+ax+b\). Zbl 1050.11091
Alaca, Şaban; Williams, Kenneth S.
1
2004
On Voronoi’s method for finding an integral basis of a cubic field. Zbl 1061.11056
Alaca, Şaban; 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
\(p\)-integral bases of algebraic number fields. Zbl 0999.11063
Alaca, Şaban
2
1999
\(p\)-integral bases of a cubic field. Zbl 0908.11048
Alaca, Saban
4
1998
all top 5

Cited by 152 Authors

17 Alaca, Şaban
17 Williams, Kenneth S.
15 Alaca, Ayşe
12 Xia, Ernest X. W.
9 Yao, Olivia Xiang Mei
8 Aygin, Zafer Selçuk
7 Ye, Dongxi
6 Köklüce, Bülent
6 Sun, Zhihong
5 Kim, Daeyeoul
5 Park, Yoon Kyung
5 Ramakrishnan, Balakrishnan
5 Sahu, Brundaban
5 Spearman, Blair Kenneth
4 Cooper, Shaun
3 Chern, Shane
3 Kanasri, Narakorn Rompurk
3 Kesicioğlu, Yavuz
3 Kim, Aeran
3 Ntienjem, Ebénézer
3 Pehlivan, Lerna
3 Singh, Anup Kumar
3 Singthongla, Patiwat
3 Sun, Zhi-Wei
2 Ahmad, Shahzad
2 Çeken, Seçil
2 Cho, Bumkyu
2 Davis, Chad Tyler
2 Doyle, Greg
2 El Bachraoui, Mohamed
2 Kendirli, Bariṣ
2 Kesicioğlu, Mücahide Nesibe
2 Laohakosol, Vichian
2 Millar, Goldwyn
2 Nakahara, Toru
2 Palmieri, John H.
2 Togbé, Alain
2 Toh, Pee Choon
2 Tosun, Cemile
2 Wang, Min
2 Wang, Yanhua
2 Xue, Jiangwei
2 Yu, Chia-Fu
2 Zhang, James J.
1 Adansie, Prince
1 Akbaş, Mehmet
1 Alan, Murat
1 Altiary, Mada
1 Andrews, George Eyre
1 Aoki, Miho
1 Baruah, Nayandeep Deka
1 Bayad, Abdelmejid
1 Bell, Jason P.
1 Cai, Tianxin
1 Chang, Sungkon
1 Chapman, Robin J.
1 Chen, Deyi
1 Chen, William Yong-Chuan
1 Chetry, Jubaraj
1 Choo, Kim-Kwang Raymond
1 Covill, Elena C.
1 Dastidar, Manosij Ghosh
1 de Jesus Nery, Genildo
1 Delmastro, Diego
1 Dumitrescu, Tiberiu
1 El Fadil, Lhoussain
1 Erban, Radek
1 Eser, Hasan
1 Feng, Rongquan
1 Forest, Simon
1 Galyautdinov, Il’darkhan Galyautdinovich
1 Gireesh, D. S.
1 Godinho, Hemar
1 Gomis, Jaume
1 Gosset, David
1 Hameed, Abdul
1 Hao, Li-Jun
1 Harrington, Joshua
1 Hong, Nankun
1 Hong, Shaofang
1 Hou, Qinghu
1 Huang, Fang
1 Husnine, Syed Muhammad
1 Issa, Ahmad
1 Javaheri, Mohammad
1 Jin, Jing
1 Jones, Lenny K.
1 Kane, Ben
1 Kaur, Mandeep
1 Khalid, Waseem
1 Kim, Chang Heon
1 Kim, Kyoungmin
1 Kim, Mingyu
1 Kim, Soeun
1 Kishi, Yasuhiro
1 Kliuchnikov, Vadym
1 Krylov, Nikolai A.
1 Kumar, Belakavadi Radhakrishna Srivatsa
1 Kwon, Soonhak
1 Kwon, Yeong-Wook
...and 52 more Authors
all top 5

Cited in 56 Serials

44 International Journal of Number Theory
13 Journal of Number Theory
12 The Ramanujan Journal
5 Journal of Mathematical Analysis and Applications
5 Integers
4 Advances in Mathematics
4 Functiones et Approximatio. Commentarii Mathematici
3 Communications in Algebra
3 European Journal of Pure and Applied Mathematics
2 Discrete Mathematics
2 Indian Journal of Pure & Applied Mathematics
2 International Journal of Mathematics and Mathematical Sciences
2 Journal of the Ramanujan Mathematical Society
2 Designs, Codes and Cryptography
2 Finite Fields and their Applications
2 Honam Mathematical Journal
2 Journal of Algebra and its Applications
2 Open Mathematics
1 Bulletin of the Australian Mathematical Society
1 Journal of Mathematical Physics
1 Rocky Mountain Journal of Mathematics
1 Mathematics of Computation
1 Mathematics Magazine
1 Acta Arithmetica
1 Czechoslovak Mathematical Journal
1 Journal of Algebra
1 Journal of the Mathematical Society of Japan
1 Kyungpook Mathematical Journal
1 Results in Mathematics
1 Transactions of the American Mathematical Society
1 Advances in Applied Mathematics
1 Acta Mathematica Hungarica
1 Bulletin of the Iranian Mathematical Society
1 International Journal of Algebra and Computation
1 New Zealand Journal of Mathematics
1 Russian Mathematics
1 Journal de Théorie des Nombres de Bordeaux
1 Turkish Journal of Mathematics
1 Selecta Mathematica. New Series
1 Abstract and Applied Analysis
1 Soft Computing
1 Journal of Inequalities and Applications
1 Annals of Combinatorics
1 Analysis (München)
1 Communications of the Korean Mathematical Society
1 Journal of High Energy Physics
1 Journal of the Australian Mathematical Society
1 Journal of Applied Mathematics
1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
1 Comptes Rendus. Mathématique. Académie des Sciences, Paris
1 Fixed Point Theory and Applications
1 Cryptography and Communications
1 Journal of Applied Mathematics & Informatics
1 Afrika Matematika
1 Journal of Mathematics
1 Research in Number Theory

Citations by Year