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

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.

arXiv comment31 pages, accepted version in "Research in Number Theory"

References in corpus (2)

• On the Rankin-Selberg integral of Kohnen and Skoruppa
• Multivariate Rankin-Selberg integrals on ${\mathrm{GL}}_4$ and $\mathrm{GU}(2,2)$