Nonvanishing of kernel functions and Poincaré series for Jacobi forms

Abstract

Y. Martin introduced a set of kernel functions for the Jacobi group to study 2m Dirichlet series associated with a Jacobi form of weight k and index m. We study nonvanishing of these kernel functions, Poincaré series and also study nonvanishing of 2m Dirichlet series associated with Jacobi form of weight k and index m.