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

Martin Raum; Jiacheng Xia

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arXiv · 1908.03616

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

Martin Raum·Jiacheng Xia

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Abstract

We 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 $\mathrm{L}$-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.

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Martin Raum, Jiacheng Xia. 2019-08-09. All modular forms of weight 2 can be expressed by Eisenstein series. https://arxiv.org/abs/1908.03616

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