{"title":"斋藤黑川升降机的质量均衡分布","authors":"Jesse Jääsaari, Stephen Lester, Abhishek Saha","doi":"10.1007/s00039-024-00690-x","DOIUrl":null,"url":null,"abstract":"<p>Let <i>F</i> be a holomorphic cuspidal Hecke eigenform for <span>\\(\\mathrm{Sp}_{4}({\\mathbb{Z}})\\)</span> of weight <i>k</i> that is a Saito–Kurokawa lift. Assuming the Generalized Riemann Hypothesis (GRH), we prove that the mass of <i>F</i> equidistributes on the Siegel modular variety as <i>k</i>⟶∞. As a corollary, we show under GRH that the zero divisors of Saito–Kurokawa lifts equidistribute as their weights tend to infinity.</p>","PeriodicalId":12478,"journal":{"name":"Geometric and Functional Analysis","volume":null,"pages":null},"PeriodicalIF":2.4000,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Mass Equidistribution for Saito-Kurokawa Lifts\",\"authors\":\"Jesse Jääsaari, Stephen Lester, Abhishek Saha\",\"doi\":\"10.1007/s00039-024-00690-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Let <i>F</i> be a holomorphic cuspidal Hecke eigenform for <span>\\\\(\\\\mathrm{Sp}_{4}({\\\\mathbb{Z}})\\\\)</span> of weight <i>k</i> that is a Saito–Kurokawa lift. Assuming the Generalized Riemann Hypothesis (GRH), we prove that the mass of <i>F</i> equidistributes on the Siegel modular variety as <i>k</i>⟶∞. As a corollary, we show under GRH that the zero divisors of Saito–Kurokawa lifts equidistribute as their weights tend to infinity.</p>\",\"PeriodicalId\":12478,\"journal\":{\"name\":\"Geometric and Functional Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2024-07-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Geometric and Functional Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00039-024-00690-x\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Geometric and Functional Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00039-024-00690-x","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
设 F 是权重为 k 的 \(\mathrm{Sp}_{4}({\mathbb{Z}})\) 的全形 Cuspidal Hecke 特征形式，它是一个 Saito-Kurokawa 提升。假定广义黎曼假说（GRH）成立，我们证明 F 的质量在西格尔模块上以 k⟶∞ 分布。作为推论，我们证明了在广义黎曼假设（GRH）下，斋藤黑川举的零除数随着其权重趋于无穷大而等分布。
Let F be a holomorphic cuspidal Hecke eigenform for \(\mathrm{Sp}_{4}({\mathbb{Z}})\) of weight k that is a Saito–Kurokawa lift. Assuming the Generalized Riemann Hypothesis (GRH), we prove that the mass of F equidistributes on the Siegel modular variety as k⟶∞. As a corollary, we show under GRH that the zero divisors of Saito–Kurokawa lifts equidistribute as their weights tend to infinity.
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Geometric And Functional Analysis (GAFA) publishes original research papers of the highest quality on a broad range of mathematical topics related to geometry and analysis.
GAFA scored in Scopus as best journal in "Geometry and Topology" since 2014 and as best journal in "Analysis" since 2016.
Publishes major results on topics in geometry and analysis.
Features papers which make connections between relevant fields and their applications to other areas.
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