Workshop: Value distribution of Hecke eigenforms , Bingrong Huang

Speaker
Bingrong Huang, Shandong University

Abstract
In this talk, we will discuss value distribution of Hecke eigenforms in the large weight limit. We will first introduce the quantum unique ergodicity theorem, and effective decorrelation of Hecke eigenforms. As consequences, we can prove an effective version of equidistribution of mass and zeros of linear combinations of Hecke eigenforms. Then we will talk about the \(L^4\) norm and joint distribution of Hecke eigenforms. We can prove some conditional results on joint moments of Hecke eigenforms under GRH and GRC, from which we obtain conditional results on a first moment and nonvanishing of the triple product L-functions.