Fourier coefficients of Jacobi Poincaré series and applications

Abstract

We define Jacobi Poincaré series over Cayley numbers and explicitly compute its Fourier coefficients. As an application, we obtain an estimate for the Fourier coefficients of a Jacobi cusp form. We also evaluate certain Petersson scalar products involving Jacobi cusp forms and Poincaré series. This evaluation yields certain special values of shifted convolution of Dirichlet series of Rankin-Selberg type associated to Jacobi cusp forms in consideration.