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arXiv · 2402.06572

Formal Siegel modular forms for arithmetic subgroups

Jan Hendrik Bruinier·Martin Raum
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Abstract

The notion of formal Siegel modular forms for an arithmetic subgroup $\Gamma$ of the symplectic group of genus $n$ is a generalization of symmetric formal Fourier-Jacobi series. Assuming an upper bound on the affine covering number of the Siegel modular variety associated with $\Gamma$, we prove that all formal Siegel modular forms are given by Fourier-Jacobi expansions of classical holomorphic Siegel modular forms. We also show that the required upper bound is always met if $2\leq n \leq 4$. As an application we consider the case of the paramodular group of squarefree level and genus $2$.

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Jan Hendrik Bruinier, Martin Raum. 2024-02-09. Formal Siegel modular forms for arithmetic subgroups. https://arxiv.org/abs/2402.06572

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