Title: Holomorphic Quantum Unique Ergodicity and Weak Subconvexity for L-functions
Abstract: Quantum unique ergodicity (QUE) describes the equidistribution of the L^2-mass of eigenfunctions of the Laplacian as their eigenvalues approach infinity. My focus lies on a specific variant known as holomorphic QUE, which concerns the distribution of the L^2-mass of normalized Hecke eigenforms of even weight k (where k ≥ 2). In 2010, Soundararajan and Holowinsky proved the equidistribution of normalized Hecke eigenforms as k tends to infinity. In my talk, I will discuss their proof ideas, explore the connection with the subconvexity problem, and present my new results on the topic.
