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 C 2 . 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.

On the analogue of Weil’s converse theorem for Jacobi forms and their lift to half-integral weight modular forms

“…Therefore, (8) and these estimates imply the existence of positive real constants K and y K such that…”

“…These objects have been investigated in [8] as they play a role in the study of certain Rankin-Selberg convolution of Siegel modular forms. The rest of the proof is an adaptation of Weil's argument which presents some technical difficulties due to the nature of Jacobi forms.…”