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

2024/07/26 by Rafail Psyroukis, Psyroukis, Rafail · 1 citation
Mathematics · #11E41 (Secondary) #11E88 #11F55 #11M41 (Primary) 11E81 #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2407.18663

openalex publication_date 2024/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Poincaré 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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