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arXiv · 2407.18663

A Fourier-Jacobi Dirichlet series for cusp forms on orthogonal groups

Rafail Psyroukis
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Abstract

We investigate a Dirichlet series involving the Fourier-Jacobi coefficients of two cusp forms $F,G$ for orthogonal groups of signature $(2,n+2)$. In the case when $F$ is a Hecke eigenform and $G$ is a Maass lift of a Poincar\'e series, we establish a connection with the standard $L$-function attached to $F$. What is more, we find explicit choices of orthogonal groups, for which we obtain a clear-cut Euler product expression for this Dirichlet series. Through our considerations, we recover a classical result for Siegel modular forms, first introduced by Kohnen and Skoruppa, but also provide a range of new examples, which can be related to other kinds of modular forms, such as paramodular, Hermitian, and quaternionic.

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Rafail Psyroukis. 2024-07-26. A Fourier-Jacobi Dirichlet series for cusp forms on orthogonal groups. https://doi.org/10.1007/s40993-025-00668-0

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