各向同性子群诱导的魏尔表示的模块形式

Pub Date : 2024-05-21 DOI:10.1016/j.jnt.2024.04.005

Manuel K.-H. Müller

{"title":"各向同性子群诱导的魏尔表示的模块形式","authors":"Manuel K.-H. Müller","doi":"10.1016/j.jnt.2024.04.005","DOIUrl":null,"url":null,"abstract":"<div>For an isotropic subgroup H of a discriminant form D there exists a lift from modular forms for the Weil representation of the discriminant form <math><msup><mrow><mi>H</mi></mrow><mrow><mo>⊥</mo></mrow></msup><mo>/</mo><mi>H</mi></math> to modular forms for the Weil representation of D. We determine a set of discriminant forms such that all modular forms for any discriminant form are induced from the discriminant forms in this set. Furthermore for any discriminant form in this set there exist modular forms that are not induced from smaller discriminant forms.</div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022314X24001082/pdfft?md5=b8470837b07e5d1a04073db4dbf9f70c&pid=1-s2.0-S0022314X24001082-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Modular forms for the Weil representation induced from isotropic subgroups\",\"authors\":\"Manuel K.-H. Müller\",\"doi\":\"10.1016/j.jnt.2024.04.005\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>For an isotropic subgroup H of a discriminant form D there exists a lift from modular forms for the Weil representation of the discriminant form <math><msup><mrow><mi>H</mi></mrow><mrow><mo>⊥</mo></mrow></msup><mo>/</mo><mi>H</mi></math> to modular forms for the Weil representation of D. We determine a set of discriminant forms such that all modular forms for any discriminant form are induced from the discriminant forms in this set. Furthermore for any discriminant form in this set there exist modular forms that are not induced from smaller discriminant forms.</div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-05-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0022314X24001082/pdfft?md5=b8470837b07e5d1a04073db4dbf9f70c&pid=1-s2.0-S0022314X24001082-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022314X24001082\",\"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/S0022314X24001082","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

对于判别式 D 的各向同性子群 H，存在着从判别式 H⊥/H 的 Weil 表示的模块形式到 D 的 Weil 表示的模块形式的提升。此外，对于这个集合中的任何判别式，都存在不是从更小的判别式诱导出来的模块形式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

Modular forms for the Weil representation induced from isotropic subgroups

For an isotropic subgroup H of a discriminant form D there exists a lift from modular forms for the Weil representation of the discriminant form $H^{⊥} / H$ to modular forms for the Weil representation of D. We determine a set of discriminant forms such that all modular forms for any discriminant form are induced from the discriminant forms in this set. Furthermore for any discriminant form in this set there exist modular forms that are not induced from smaller discriminant forms.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助