# The eighth moment of $\Gamma_1(q)$ L-functions

Date: Mon, Nov 6, 2023

Location: PIMS, University of Lethbridge, Online, Zoom

Conference: Analytic Aspects of L-functions and Applications to Number Theory

Subject: Mathematics, Number Theory

Class: Scientific

CRG: L-Functions in Analytic Number Theory

### Abstract:

In this talk, I will discuss my on-going joint work with Xiannan Li on an unconditional asymptotic formula for the eighth moment of $\Gamma_1(q)$ L-functions, which are associated with eigenforms for the congruence subgroups $\Gamma_1(q)$. Similar to a large family of Dirichlet L-functions, the family of $\Gamma_1(q)$ L-functions has a size around $q^2$ while the conductor is of size $q$. An asymptotic large sieve of the family is available by the work of Iwaniec and Xiaoqing Li, and they observed that this family of harmonics is not perfectly orthogonal. This introduces certain subtleties in our work.