Value distribution of Hecke eigenforms and moments of L-functions

In this talk, we study the value distribution of Hecke eigenforms in the large
weight limit. We begin with an introduction to the quantum unique ergodicity
(QUE) theorem and its application to the equidistribution of zeros of Hecke
eigenforms. We then focus on their joint value distribution. In particular, we
establish asymptotic formulas for certain low-degree mixed moments. Our
approach is based on estimates for moments of $L$-functions.