**Soumya Das**

TIFR

October 28, 2010

**Non vanishing of Jacobi Poincar\'e series and the structure of Hermitian Jacobi forms**:
It is known that the Poincar\'e series span the space of cusp forms
for several types of modular forms. However it is in general an open question to decide which of them do not vanish identically. We give some sufficient conditions for the non vanishing of Poincar\'e series for the Jacobi group over the integers. We also discuss several structural properties of Hermitian Jacobi forms and some questions related to their structure as a module over the algebra of elliptic modular forms.