A characterization of Jacobi cusp forms of certain types

Abstract

In this dissertation, a sufficient condition for a Jacobi form f of weight k, index m and level N (m,N: both squarefree with (2m,N) = 1) to be a Jacobi cusp form will be given. In order to accomplish this we will investigate the structure of the Jacobi Eisenstein space and compute the Fourier coefficients of the Jacobi Eisenstein series. Using these we will give a proof of the main theorem.