{"title":"HIGHER MOMENT FORMULAE AND LIMITING DISTRIBUTIONS OF LATTICE POINTS","authors":"Mahbub Alam, Anish Ghosh, Jiyoung Han","doi":"10.1017/s147474802300035x","DOIUrl":null,"url":null,"abstract":"We establish higher moment formulae for Siegel transforms on the space of affine unimodular lattices as well as on certain congruence quotients of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S147474802300035X_inline1.png\" /> <jats:tex-math> $\\mathrm {SL}_d({\\mathbb {R}})$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. As applications, we prove functional central limit theorems for lattice point counting for affine and congruence lattices using the method of moments.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":"23 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Institute of Mathematics of Jussieu","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s147474802300035x","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 4
Abstract
We establish higher moment formulae for Siegel transforms on the space of affine unimodular lattices as well as on certain congruence quotients of $\mathrm {SL}_d({\mathbb {R}})$ . As applications, we prove functional central limit theorems for lattice point counting for affine and congruence lattices using the method of moments.
期刊介绍：
The Journal of the Institute of Mathematics of Jussieu publishes original research papers in any branch of pure mathematics; papers in logic and applied mathematics will also be considered, particularly when they have direct connections with pure mathematics. Its policy is to feature a wide variety of research areas and it welcomes the submission of papers from all parts of the world. Selection for publication is on the basis of reports from specialist referees commissioned by the Editors.
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