Kaisa Matomäki: Mollifying Dirichlet L-functions and their derivatives

Abstract:

I will first discuss how mollified moments have been used to study non-vanishing of Dirichlet L-functions. Then I will describe some observations concerning mollifiers. In the final part I will briefly show how some of these observations can be used to improve on the known non-vanishing proportion of \(L'(1/2, \chi)\) (and of higher derivatives). The talk is based on on-going joint work with Martin Čech.