{"title":"网格中的轨道","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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-07-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022314X24001549\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022314X24001549","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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.
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