Quotients of {$L$}-functions

Abstract

In this paper a certain type of Dirichlet series, attached to a pair of Jacobi forms and Siegel modular forms is studied. It is shown that this series can be analyzed by a new variant of the Rankin-Selberg method. We prove that for eigenforms the Dirichlet series have an Euler product and we calculate all the local $L$-factors. Globally this Euler product is essentially the quotient of the standard $L$-functions of the involved Jacobi- and Siegel modular form.