Cusp forms for congruence subgroups of 𝑆𝑝_{𝑛}(ℤ) and theta functions

Kopeliovich, Yaacov

doi:10.1090/S0002-9947-98-01820-0

Cusp forms for congruence subgroups of $Sp_n(\mathbb {Z})$ and theta functions
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Trans. Amer. Math. Soc. 350 (1998), 3107-3118 Request permission

Abstract:

In this paper we use theta functions with rational characteristic to construct cusp forms for congruence subgroups $\Gamma _g(p)$ of $Sp(g,\mathbb {Z})$.The action of the quotient group $Sp(g,\mathbb {Z}_p)$ on these forms is conjugate to the linear action of $Sp(g,\mathbb {Z}_p)$ on $(\mathbb {Z}_p)^{2g}$. We show that these forms are higher-dimensional analogues of the Fricke functions.

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