{"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}
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Abstract
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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