The non-vanishing of L-functions at the central point s = 1/2 is a fundamental problem in number theory, with far-reaching consequences related to the Birch and Swinnerton-Dyer conjecture, the Landau-Siegel zero problem, and the distribution of low-lying zeros. In this talk, I will provide a historical overview of the problem, present the mollifier method, and, if time permits, discuss some recent advances in this area. This is joint work with Alexandru Zaharescu.
Talk by Debmalya Basak.