All modular forms of weight 2 can be expressed by Eisenstein series

Author:

Raum Martin,Xia Jiacheng

Abstract

AbstractWe show that every elliptic modular form of integral weight greater than 1 can be expressed as linear combinations of products of at most two cusp expansions of Eisenstein series. This removes the obstruction of nonvanishing central $$\mathrm{L}$$ L -values present in all previous work. For weights greater than 2, we refine our result further, showing that linear combinations of products of exactly two cusp expansions of Eisenstein series suffice.

Funder

Vetenskapsrådet

Publisher

Springer Science and Business Media LLC

Subject

Algebra and Number Theory

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Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Rankin–Cohen brackets of vector valued Eisenstein series;The Ramanujan Journal;2023-06-22

2. On the computation of general vector-valued modular forms;Mathematics of Computation;2023-05-23

3. A dominated convergence theorem for Eisenstein series;Annales mathématiques du Québec;2021-03-18

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