{"title":"Orbits in lattices","authors":"Matthew Dawes","doi":"10.1016/j.jnt.2024.06.013","DOIUrl":null,"url":null,"abstract":"<div><p>Let <em>L</em> be a lattice. We exhibit algorithms for calculating Tits buildings and orbits of vectors in <em>L</em> for certain subgroups of the orthogonal group <span><math><mi>O</mi><mo>(</mo><mi>L</mi><mo>)</mo></math></span>. We discuss how these algorithms can be applied to determine the configuration of boundary components in the Baily-Borel compactification of orthogonal modular varieties and to improve the performance of computer arithmetic of orthogonal modular forms.</p></div>","PeriodicalId":50110,"journal":{"name":"Journal of Number Theory","volume":"265 ","pages":"Pages 181-207"},"PeriodicalIF":0.6000,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Number Theory","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022314X24001549","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let L be a lattice. We exhibit algorithms for calculating Tits buildings and orbits of vectors in L for certain subgroups of the orthogonal group . We discuss how these algorithms can be applied to determine the configuration of boundary components in the Baily-Borel compactification of orthogonal modular varieties and to improve the performance of computer arithmetic of orthogonal modular forms.
期刊介绍：
The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field.
The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory.
Starting in May 2019, JNT will have a new format with 3 sections:
JNT Prime targets (possibly very long with complete proofs) high impact papers. Articles published in this section will be granted 1 year promotional open access.
JNT General Section is for shorter papers. We particularly encourage submission from junior researchers. Every attempt will be made to expedite the review process for such submissions.
Computational JNT . This section aims to provide a forum to disseminate contributions which make significant use of computer calculations to derive novel number theoretic results. There will be an online repository where supplementary codes and data can be stored.
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