Theta products and eta quotients of level 24 and weight 2
We find bases for the spaces M2(Γ0(24),(d⋅))M2(Γ0(24),(d⋅)) (d=1,8,12,24d=1,8,12,24) of modular forms. We determine the Fourier coefficients of all 3535 theta products φ[a1,a2,a3,a4](z)φ[a1,a2,a3,a4](z) in these spaces. We then deduce formulas for the number of representations of a positive integer...
| Main Authors: | , , |
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| Format: | Journal Article |
| Language: | English |
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2017
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| Online Access: | https://hdl.handle.net/10356/84889 http://hdl.handle.net/10220/43604 |
| _version_ | 1811676866347532288 |
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| author | Alaca, Ayşe Alaca, Şaban Aygin, Zafer Selcuk |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Alaca, Ayşe Alaca, Şaban Aygin, Zafer Selcuk |
| author_sort | Alaca, Ayşe |
| collection | NTU |
| description | We find bases for the spaces M2(Γ0(24),(d⋅))M2(Γ0(24),(d⋅)) (d=1,8,12,24d=1,8,12,24) of modular forms. We determine the Fourier coefficients of all 3535 theta products φ[a1,a2,a3,a4](z)φ[a1,a2,a3,a4](z) in these spaces. We then deduce formulas for the number of representations of a positive integer nn by diagonal quaternary quadratic forms with coefficients 11, 22, 33 or 66 in a uniform manner, of which 1414 are Ramanujan's universal quaternary quadratic forms. We also find all the eta quotients in the Eisenstein spaces E2(Γ0(24),(d⋅))E2(Γ0(24),(d⋅)) (d=1,8,12,24d=1,8,12,24) and give their Fourier coefficients. |
| first_indexed | 2024-10-01T02:28:17Z |
| format | Journal Article |
| id | ntu-10356/84889 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T02:28:17Z |
| publishDate | 2017 |
| record_format | dspace |
| spelling | ntu-10356/848892023-02-28T19:28:07Z Theta products and eta quotients of level 24 and weight 2 Alaca, Ayşe Alaca, Şaban Aygin, Zafer Selcuk School of Physical and Mathematical Sciences Eta quotients Dedekind eta function We find bases for the spaces M2(Γ0(24),(d⋅))M2(Γ0(24),(d⋅)) (d=1,8,12,24d=1,8,12,24) of modular forms. We determine the Fourier coefficients of all 3535 theta products φ[a1,a2,a3,a4](z)φ[a1,a2,a3,a4](z) in these spaces. We then deduce formulas for the number of representations of a positive integer nn by diagonal quaternary quadratic forms with coefficients 11, 22, 33 or 66 in a uniform manner, of which 1414 are Ramanujan's universal quaternary quadratic forms. We also find all the eta quotients in the Eisenstein spaces E2(Γ0(24),(d⋅))E2(Γ0(24),(d⋅)) (d=1,8,12,24d=1,8,12,24) and give their Fourier coefficients. MOE (Min. of Education, S’pore) Accepted version 2017-08-17T05:25:11Z 2019-12-06T15:53:07Z 2017-08-17T05:25:11Z 2019-12-06T15:53:07Z 2017 Journal Article Alaca, A., Alaca, Ş., & Aygin, Z. S. (2017). Theta products and eta quotients of level 24 and weight 2. Functiones et Approximatio, Commentarii Mathematici, in press. 0208-6573 https://hdl.handle.net/10356/84889 http://hdl.handle.net/10220/43604 10.7169/facm/1628 en Functiones et Approximatio, Commentarii Mathematici © 2017 Adam Mickiewicz University, Faculty of Mathematics and Computer Science. This is the author created version of a work that has been peer reviewed and accepted for publication in Functiones et Approximatio, Commentarii Mathematici, by Adam Mickiewicz University, Faculty of Mathematics and Computer Science. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.7169/facm/1628]. 29 p. application/pdf |
| spellingShingle | Eta quotients Dedekind eta function Alaca, Ayşe Alaca, Şaban Aygin, Zafer Selcuk Theta products and eta quotients of level 24 and weight 2 |
| title | Theta products and eta quotients of level 24 and weight 2 |
| title_full | Theta products and eta quotients of level 24 and weight 2 |
| title_fullStr | Theta products and eta quotients of level 24 and weight 2 |
| title_full_unstemmed | Theta products and eta quotients of level 24 and weight 2 |
| title_short | Theta products and eta quotients of level 24 and weight 2 |
| title_sort | theta products and eta quotients of level 24 and weight 2 |
| topic | Eta quotients Dedekind eta function |
| url | https://hdl.handle.net/10356/84889 http://hdl.handle.net/10220/43604 |
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