Abstracts

  • 14:00-15:00, Asbjørn Nordentoft

Title: Wide moments of automorphic L-functions

Abstract: I will explain how to calculate certain types of "wide moments" of automorphic L-function, which in many cases are easier to handle due to connections to automorphic periods.

In particular, we will consider the case of Dirchlet L-functions as well as GL_2 twisted by class group characters of imaginary quadratic fields. Here the "wide moments" are connected to, respectively, analytic properties of Lerch zeta functions and equidistribution of Heegner points using Waldspurger's formula. We will also present applications to non-vanishing.

  • 15:15-16:15, Youness Lamzouri

Title: Zeros of linear combinations of L-functions near the critical line

  • 16:30-17:30, Emma Bailey

Title: Extreme values and large deviations of random matrix polynomials and L-functions

Abstract: This talk will present results on generalised moments and large deviations for zeta, influenced by random matrix calculations. Such a connection is motivated by the work of Keating and Snaith, Katz and Sarnak. In particular, we demonstrate that the ‘moments of moments’ of the zeta-function should satisfy a Fyodorov-Keating conjecture (via a conjectural integral form). Additionally, motived by a conjecture of Radziwiłł, we also present numerical evidence towards random matrix corrections to large-deviations of Selberg’s CLT.