Colloquium abstracts

Moni Kumari
TIFR, Mumbai
May 9, 2019

Non-vanishing of Hilbert Poincare series:  Modular forms play a very important role in the classical as well as in modern number theory. In the theory of modular forms, there is a very important family of functions called Poincare series. The vanishing or non-vanishing of these functions for the full modular group (and also for its congruence subgroups) is an open problem. In particular, the non-vanishing of Poincare series is related to the famous conjecture of Lehmer about the Ramanujan tau function, which is one of the classical open problem in this area. In this talk, I will first review some of the known results for the non-vanishing problem and then I will talk about its natural generalization to the case of Hilbert modular forms.