Holomorphic quantum unique ergodicity and weak subconvexity for L-functions

Quantum unique ergodicity (QUE) describes the equidistribution of the L2-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 L2-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 this talk, I will present my new results on the topic, namely, an effective holomorphic QUE and an effective decorrelation of Hecke eigenforms in the level aspect. To prove these results, I refine Soundararajan's weak subconvexity bound for Rankin--Selberg  L-functions, and some proof ideas of this refinement will be discussed during the talk.