Quantum variance of Maass-Hecke cusp forms
type: Item
instance of: scholarly article
title: Quantum variance of Maass-Hecke cusp forms
zbMATH Open document ID: 1198.81138
author: Peng Zhao
published in: Communications in Mathematical Physics
publication date: 2010-07-06T00:00:00Z
full work available at URL: http://rave.ohiolink.edu/etdc/view
review text: 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.
Mathematics Subject Classification ID: 81S99
Mathematics Subject Classification ID: 81S25
zbMATH DE Number: 5731326
zbMATH Keywords: quantum variance
zbMATH Keywords: classical variance
zbMATH Keywords: Poincare series
zbMATH Keywords: Maass-Hecke L-functions
reviewed by: Guy Jumarie
MaRDI profile type: Publication
OpenAlex ID: W2035749684
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DOI: 10.1007/S00220-009-0943-9
description: scientific article; zbMATH DE number 5731326