Number Theory Seminar

Speaker: Martin Cech (Concordia University)

Title: Ratios conjectures and multiple Dirichlet series

Abstract: Conrey, Farmer, and Zirnbauer conjectured asymptotics for ratios of products of shifted L-functions averaged over a family. These conjectures are very powerful in that they give us information about many other statistics, such as information about the distribution of zeros of the L-functions or various moments. During the talk, we will show how to use multiple Dirichlet series to conditionally under GRH prove the conjectures in some ranges of the shifts for the family of quadratic Dirichlet L-functions.