{"title":"The Prime Geodesic Theorem in Arithmetic Progressions","authors":"Dimitrios Chatzakos, Gergely Harcos, Ikuya Kaneko","doi":"10.1093/imrn/rnae198","DOIUrl":null,"url":null,"abstract":"We address the prime geodesic theorem in arithmetic progressions and resolve conjectures of Golovchanskiĭ–Smotrov (1999). In particular, we prove that the traces of closed geodesics on the modular surface do not equidistribute in the reduced residue classes of a given modulus.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Mathematics Research Notices","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1093/imrn/rnae198","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We address the prime geodesic theorem in arithmetic progressions and resolve conjectures of Golovchanskiĭ–Smotrov (1999). In particular, we prove that the traces of closed geodesics on the modular surface do not equidistribute in the reduced residue classes of a given modulus.
期刊介绍：
International Mathematics Research Notices provides very fast publication of research articles of high current interest in all areas of mathematics. All articles are fully refereed and are judged by their contribution to advancing the state of the science of mathematics.
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