Till innehåll på sidan

Adrian Diaconu: Moments and multiple Dirichlet series

Tid: On 2018-10-24 kl 11.00 - 12.00

Plats: Room F11, KTH

Medverkande: Adrian Diaconu (University of Minnesota)

Exportera till kalender

Abstract: In the 1980's the idea emerged that it could be useful to tie together a family of related L-functions to create a double, or multiple, Dirichlet series, which could be used to study the average behavior of the original family of L-functions. The local structure of these multiple Dirichlet series shows a rich connection to the theory of automorphic forms (i.e., Whittaker functions on p-adic groups and their covers are the fundamental objects), and representation theory.

In this talk, I will focus on the most important case, namely the multiple Dirichlet series associated to moments of L-functions. I will discuss the connection between the local parts of these series and the compactifications of certain moduli spaces of curves, and how this information can be combined with the (conjectural in general) analytic continuation of the multiple Dirichlet series to obtain precise asymptotics for moments, for example, of the classical family of quadratic Dirichlet L-functions. (Based on recent joint work with Vicentiu Pasol.)