New variants of arithmetic quantum ergodicity

2024/03/21 by Peter Humphries, Humphries, Peter, Jesse Thorner +1
Computer Science · Physics and Astronomy · #FOS: Mathematics #Number Theory (math.NT) #Quantum Computing Algorithms and Architecture #Quantum Mechanics and Applications

paper · pdf · doi:10.48550/arxiv.2403.14591

openalex publication_date 2024/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish two new variants of arithmetic quantum ergodicity. The first is for self-dual GL₂ Hecke-Maass newforms over ℚ as the level and Laplace eigenvalue vary jointly. The second is a nonsplit analogue wherein almost all restrictions of Hilbert (respectively Bianchi) Hecke-Maass cusp forms to the modular surface dissipate as their Laplace eigenvalues grow.

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