On characteristic twists of multiple Dirichlet series associated to Siegel cusp forms

Abstract

We define a twisted two complex variables Rankin-Selberg convolution of Siegel cusp forms of degree 2. We find its group of functional equations and prove its analytic continuation to ℂ2. As an application we obtain a non-vanishing result for special values of the Fourier Jacobi coefficients. We also prove the analytic properties for the characteristic twists of convolutions of Jacobi cusp forms. © Springer-Verlag 2008.