Asbjørn Nordentoft (University of Bonn): Wide moments of automorphic $L$-functions

Abstract: In this talk, we will talk about how to calculate certain types of "wide moments" of automorphic $L$-functions, which in many cases can be calculated using geometrically flavoured methods due to connections to automorphic periods.

In particular we will consider the case of Rankin-Selberg $L$-functions of $GL_2$ automorphic forms twisted by class group characters of imaginary quadratic fields, in which case the "wide moments" are connected to equidistribution of Heegner points using Waldspurger's formula. We will also present applications to non-vanishing.

The link for the talk is https://zoom.us/j/94752830725, the password is the order of $\mathrm{SL}_2(\mathbb{F}_{97})$.