Computing Classical Modular Forms for Arbitrary Congruence Subgroups

Fuente: arXiv
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1. Verfasser: Assaf, Eran
Format: Preprint
Veröffentlicht: 2020
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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