Alexandru Popa: Non-vanishing of central values for Hecke L-functions of r-th order characters

I show how the mollification method, applied to the first and second moments within the framework of multiple Dirichlet series, yields an explicit, positive proportion of non-vanishing for the central $L$-values of $r$-th order Hecke characters. This is joint work with Adrian Diaconu, Bogdan Ion and Vicentiu Pasol.