Binomial convolution sum of divisor functions associated with Dirichlet character modulo 8
In this article, we compute binomial convolution sums of divisor functions associated with the Dirichlet character modulo 8, which is the remaining primitive Dirichlet character modulo powers of 2 yet to be considered. To do this, we provide an explicit expression of a general modular form of even w...
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| Format: | Article |
| Language: | English |
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De Gruyter
2024-11-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2024-0089 |
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| author | Jin Seokho Park Ho |
| author_facet | Jin Seokho Park Ho |
| author_sort | Jin Seokho |
| collection | DOAJ |
| description | In this article, we compute binomial convolution sums of divisor functions associated with the Dirichlet character modulo 8, which is the remaining primitive Dirichlet character modulo powers of 2 yet to be considered. To do this, we provide an explicit expression of a general modular form of even weight for Γ0(32){\Gamma }_{0}\left(32) in terms of its basis, and use an identity of Huard, Ou, Spearman, and Williams. As an application, we also compute the number of representations by quadratic forms under parity conditions. |
| format | Article |
| id | doaj-art-c3c68cd5bf134bbcaf8225575468bdd9 |
| institution | Kabale University |
| issn | 2391-5455 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj-art-c3c68cd5bf134bbcaf8225575468bdd92024-11-25T11:18:19ZengDe GruyterOpen Mathematics2391-54552024-11-0122125615210.1515/math-2024-0089Binomial convolution sum of divisor functions associated with Dirichlet character modulo 8Jin Seokho0Park Ho1Department of Mathematics, Chung-Ang University, 84 Heukseok-ro, Seoul 06974, Republic of KoreaDepartment of Mathematics, Dongguk University, 30 Pildong-ro 1-gil, Jung-gu, Seoul 04620, Republic of KoreaIn this article, we compute binomial convolution sums of divisor functions associated with the Dirichlet character modulo 8, which is the remaining primitive Dirichlet character modulo powers of 2 yet to be considered. To do this, we provide an explicit expression of a general modular form of even weight for Γ0(32){\Gamma }_{0}\left(32) in terms of its basis, and use an identity of Huard, Ou, Spearman, and Williams. As an application, we also compute the number of representations by quadratic forms under parity conditions.https://doi.org/10.1515/math-2024-0089divisor functiondirichlet characterconvolution sumarithmetic identityeisenstein series11a2511e2511f1111f2011f30 |
| spellingShingle | Jin Seokho Park Ho Binomial convolution sum of divisor functions associated with Dirichlet character modulo 8 Open Mathematics divisor function dirichlet character convolution sum arithmetic identity eisenstein series 11a25 11e25 11f11 11f20 11f30 |
| title | Binomial convolution sum of divisor functions associated with Dirichlet character modulo 8 |
| title_full | Binomial convolution sum of divisor functions associated with Dirichlet character modulo 8 |
| title_fullStr | Binomial convolution sum of divisor functions associated with Dirichlet character modulo 8 |
| title_full_unstemmed | Binomial convolution sum of divisor functions associated with Dirichlet character modulo 8 |
| title_short | Binomial convolution sum of divisor functions associated with Dirichlet character modulo 8 |
| title_sort | binomial convolution sum of divisor functions associated with dirichlet character modulo 8 |
| topic | divisor function dirichlet character convolution sum arithmetic identity eisenstein series 11a25 11e25 11f11 11f20 11f30 |
| url | https://doi.org/10.1515/math-2024-0089 |
| work_keys_str_mv | AT jinseokho binomialconvolutionsumofdivisorfunctionsassociatedwithdirichletcharactermodulo8 AT parkho binomialconvolutionsumofdivisorfunctionsassociatedwithdirichletcharactermodulo8 |