Computing Classical Modular Forms for Arbitrary Congruence Subgroups
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arXiv
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866911499167989760 |
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| author | Assaf, Eran |
| author_facet | Assaf, Eran |
| contents | In this paper, we prove the existence of an efficient algorithm for the computation of $q$-expansions of modular forms of weight $k$ and level $Γ$, where $Γ\subseteq SL_{2}({\mathbb{Z}})$ is an arbitrary congruence subgroup. We also discuss some practical aspects and provide the necessary theoretical background. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2002_07212 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Computing Classical Modular Forms for Arbitrary Congruence Subgroups Assaf, Eran Number Theory 11F11 (Primary) 11Y40, 11G18 (Secondary) In this paper, we prove the existence of an efficient algorithm for the computation of $q$-expansions of modular forms of weight $k$ and level $Γ$, where $Γ\subseteq SL_{2}({\mathbb{Z}})$ is an arbitrary congruence subgroup. We also discuss some practical aspects and provide the necessary theoretical background. |
| title | Computing Classical Modular Forms for Arbitrary Congruence Subgroups |
| topic | Number Theory 11F11 (Primary) 11Y40, 11G18 (Secondary) |
| url | https://arxiv.org/abs/2002.07212 |