{"title":"New Variants of Arithmetic Quantum Ergodicity","authors":"Peter Humphries, Jesse Thorner","doi":"10.1007/s00220-024-05203-3","DOIUrl":null,"url":null,"abstract":"<div><p>We establish two new variants of arithmetic quantum ergodicity. The first is for self-dual <span>\\(\\textrm{GL}_2\\)</span> Hecke–Maaß newforms over <span>\\(\\mathbb {Q}\\)</span> 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.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"406 3","pages":""},"PeriodicalIF":2.2000,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05203-3.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s00220-024-05203-3","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
We establish two new variants of arithmetic quantum ergodicity. The first is for self-dual \(\textrm{GL}_2\) Hecke–Maaß newforms over \(\mathbb {Q}\) 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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The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.
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