Quantum variance of Maass-Hecke cusp forms
This article is an asymptotical study of the quantum variance which has been introduced by Zelditch to describe the fluctuations of quantum observables. Its main result is a generalization to Maass cusp forms of results previously obtained by Luo and Sarnak on quantum variance for Hecke eigenforms. The proof of the theorem is based on the properties of a non-negative Hermitian form \(B\) which characterizes the considered system, and the result is obtained by a combination of Watson's formula, Rankin-Selberg theory and the Kuznetsov formula.
scientific article; zbMATH DE number 5731326
scientific article