Work

Subconvexity implies effective quantum unique ergodicity for Hecke–Maaß cusp forms on SL2(ℤ)∖SL2(ℝ)

Year: 2024

Type: article

Abstract: It is a folklore result in arithmetic quantum chaos that quantum unique ergodicity on the modular surface with an effective rate of convergence follows from subconvex bounds for certain triple product L-functions.The physical space manifestation of this result, namely the equidistribution of mass of Hecke-Maaß cusp forms, was proven to follow from subconvexity by Watson, whereas the phase space manifestation of quantum unique ergodicity has only previously appeared in the literature for Eisenstein series via work of Jakobson.We detail the analogous phase space result for Hecke-Maaß cusp forms.The proof relies on the Watson-Ichino triple product formula together with a careful analysis of certain archimedean integrals of Whittaker functions.

Source: Essential Number Theory

DOI: 10.2140/ent.2024.3.101

Authors: Ankit Bisain, Peter Humphries, Andrei Mandelshtam, Noah Walsh, Xun Wang

Institutions: Massachusetts Institute of Technology, University of Virginia, Stanford University, Northwestern University

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: National Science Foundation, National Security Agency, Templeton World Charity Foundation

Awards: Equidistribution, Period Integrals of Automorphic Forms, and Subconvexity, G7685336770, G7845798442, REU Site: Arithmetic Geometry, Number Theory, and Representation Theory at the University of Virginia, REU Site: Algebra and Number Theory at Emory University