{"title":"有效映射类群动力学，I：Teichmüller空间中的格点计数","authors":"Francisco Arana-Herrera","doi":"10.1215/00127094-2022-0066","DOIUrl":null,"url":null,"abstract":"We prove a quantitative estimate with a power saving error term for the number of points in a mapping class group orbit of Teichm\\\"uller space that lie within a Teichm\\\"uller metric ball of given center and large radius. Estimates of the same kind are also proved for sector and bisector counts. These estimates effectivize asymptotic counting results of Athreya, Bufetov, Eskin, and Mirzakhani.","PeriodicalId":11447,"journal":{"name":"Duke Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":2.3000,"publicationDate":"2020-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Effective mapping class group dynamics, I: Counting lattice points in Teichmüller space\",\"authors\":\"Francisco Arana-Herrera\",\"doi\":\"10.1215/00127094-2022-0066\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove a quantitative estimate with a power saving error term for the number of points in a mapping class group orbit of Teichm\\\\\\\"uller space that lie within a Teichm\\\\\\\"uller metric ball of given center and large radius. Estimates of the same kind are also proved for sector and bisector counts. These estimates effectivize asymptotic counting results of Athreya, Bufetov, Eskin, and Mirzakhani.\",\"PeriodicalId\":11447,\"journal\":{\"name\":\"Duke Mathematical Journal\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2020-10-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Duke Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1215/00127094-2022-0066\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Duke Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1215/00127094-2022-0066","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Effective mapping class group dynamics, I: Counting lattice points in Teichmüller space
We prove a quantitative estimate with a power saving error term for the number of points in a mapping class group orbit of Teichm\"uller space that lie within a Teichm\"uller metric ball of given center and large radius. Estimates of the same kind are also proved for sector and bisector counts. These estimates effectivize asymptotic counting results of Athreya, Bufetov, Eskin, and Mirzakhani.
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