**Ritabrata Munshi**

Rutgers University, U.S.A.

August 6, 2009

**Non-vanishing of L-functions**:
Non-vanishing of L-functions inside the critical strip is an important problem in number theory. Indeed it is related with deep arithmetic problems like distribution of prime numbers and distribution of rational points on varieties. In this talk I will approach the problem from the point of view of analytic number theory. I will briefly discuss the scope and limitations of analytic methods, and possible ways to overcome these limitations.