{"title":"𝐸_{7,3}型例外群上爱森斯坦数列的𝑝-adic极限","authors":"Hidenori Katsurada, Henry Kim","doi":"10.1090/proc/16866","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we show that the <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=\"application/x-tex\">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-adic limit of a family of Eisenstein series on the exceptional domain where the exceptional group of type <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper E Subscript 7 comma 3\"> <mml:semantics> <mml:msub> <mml:mi>E</mml:mi> <mml:mrow> <mml:mn>7</mml:mn> <mml:mo>,</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> <mml:annotation encoding=\"application/x-tex\">E_{7,3}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> acts is an ordinary modular form for a congruence subgroup.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"𝑝-adic limit of the Eisenstein series on the exceptional group of type 𝐸_{7,3}\",\"authors\":\"Hidenori Katsurada, Henry Kim\",\"doi\":\"10.1090/proc/16866\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we show that the <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"p\\\"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=\\\"application/x-tex\\\">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-adic limit of a family of Eisenstein series on the exceptional domain where the exceptional group of type <inline-formula content-type=\\\"math/mathml\\\"> <mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper E Subscript 7 comma 3\\\"> <mml:semantics> <mml:msub> <mml:mi>E</mml:mi> <mml:mrow> <mml:mn>7</mml:mn> <mml:mo>,</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msub> <mml:annotation encoding=\\\"application/x-tex\\\">E_{7,3}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> acts is an ordinary modular form for a congruence subgroup.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-03-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/proc/16866\",\"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://doi.org/10.1090/proc/16866","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
在本文中，我们证明了在类型为 E 7 , 3 E_{7,3} 的卓越群作用的卓越域上，爱森斯坦级数族的 p p -adic 极限是一个全等子群的普通模态。
𝑝-adic limit of the Eisenstein series on the exceptional group of type 𝐸_{7,3}
In this paper, we show that the pp-adic limit of a family of Eisenstein series on the exceptional domain where the exceptional group of type E7,3E_{7,3} acts is an ordinary modular form for a congruence subgroup.
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