{"title":"超越新形式的超正则问题","authors":"EDGAR ASSING","doi":"10.1017/s0305004124000021","DOIUrl":null,"url":null,"abstract":"<p>In this paper we take up the classical sup-norm problem for automorphic forms and view it from a new angle. Given a twist minimal automorphic representation <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240311161759314-0086:S0305004124000021:S0305004124000021_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$\\pi$</span></span></img></span></span> we consider a special small <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240311161759314-0086:S0305004124000021:S0305004124000021_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$\\mathrm{GL}_2(\\mathbb{Z}_p)$</span></span></img></span></span>-type <span>V</span> in <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240311161759314-0086:S0305004124000021:S0305004124000021_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$\\pi$</span></span></img></span></span> and prove global sup-norm bounds for an average over an orthonormal basis of <span>V</span>. We achieve a non-trivial saving when the dimension of <span>V</span> grows.</p>","PeriodicalId":18320,"journal":{"name":"Mathematical Proceedings of the Cambridge Philosophical Society","volume":"22 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The sup-norm problem beyond the newform\",\"authors\":\"EDGAR ASSING\",\"doi\":\"10.1017/s0305004124000021\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper we take up the classical sup-norm problem for automorphic forms and view it from a new angle. Given a twist minimal automorphic representation <span><span><img data-mimesubtype=\\\"png\\\" data-type=\\\"\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240311161759314-0086:S0305004124000021:S0305004124000021_inline1.png\\\"><span data-mathjax-type=\\\"texmath\\\"><span>$\\\\pi$</span></span></img></span></span> we consider a special small <span><span><img data-mimesubtype=\\\"png\\\" data-type=\\\"\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240311161759314-0086:S0305004124000021:S0305004124000021_inline2.png\\\"><span data-mathjax-type=\\\"texmath\\\"><span>$\\\\mathrm{GL}_2(\\\\mathbb{Z}_p)$</span></span></img></span></span>-type <span>V</span> in <span><span><img data-mimesubtype=\\\"png\\\" data-type=\\\"\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240311161759314-0086:S0305004124000021:S0305004124000021_inline3.png\\\"><span data-mathjax-type=\\\"texmath\\\"><span>$\\\\pi$</span></span></img></span></span> and prove global sup-norm bounds for an average over an orthonormal basis of <span>V</span>. We achieve a non-trivial saving when the dimension of <span>V</span> grows.</p>\",\"PeriodicalId\":18320,\"journal\":{\"name\":\"Mathematical Proceedings of the Cambridge Philosophical Society\",\"volume\":\"22 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-03-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Proceedings of the Cambridge Philosophical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/s0305004124000021\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Proceedings of the Cambridge Philosophical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s0305004124000021","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
摘要
在本文中，我们从一个新的角度探讨了自动形式的经典超规范问题。给定一个扭转最小自形表示 $\pi$ ，我们考虑 $\pi$ 中一个特殊的小 $\mathrm{GL}_2(\mathbb{Z}_p)$ 型 V，并证明 V 的正交基础上的平均的全局超规范边界。
In this paper we take up the classical sup-norm problem for automorphic forms and view it from a new angle. Given a twist minimal automorphic representation $\pi$ we consider a special small $\mathrm{GL}_2(\mathbb{Z}_p)$-type V in $\pi$ and prove global sup-norm bounds for an average over an orthonormal basis of V. We achieve a non-trivial saving when the dimension of V grows.
期刊介绍：
Papers which advance knowledge of mathematics, either pure or applied, will be considered by the Editorial Committee. The work must be original and not submitted to another journal.
$\pi$ we consider a special small 
$\mathrm{GL}_2(\mathbb{Z}_p)$-type V in 
$\pi$ and prove global sup-norm bounds for an average over an orthonormal basis of V. We achieve a non-trivial saving when the dimension of V grows.
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