On the Gross–Prasad conjecture with its refinement for (SO(5), SO(2)) and the generalized Böcherer conjecture

IF 1.3 1区 数学 Q1 MATHEMATICS Compositio Mathematica Pub Date : 2024-09-13 DOI:10.1112/s0010437x24007267
Masaaki Furusawa, Kazuki Morimoto
{"title":"On the Gross–Prasad conjecture with its refinement for (SO(5), SO(2)) and the generalized Böcherer conjecture","authors":"Masaaki Furusawa, Kazuki Morimoto","doi":"10.1112/s0010437x24007267","DOIUrl":null,"url":null,"abstract":"<p>We investigate the Gross–Prasad conjecture and its refinement for the Bessel periods in the case of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240912063150983-0859:S0010437X24007267:S0010437X24007267_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$(\\mathrm {SO}(5), \\mathrm {SO}(2))$</span></span></img></span></span>. In particular, by combining several theta correspondences, we prove the Ichino–Ikeda-type formula for any tempered irreducible cuspidal automorphic representation. As a corollary of our formula, we prove an explicit formula relating certain weighted averages of Fourier coefficients of holomorphic Siegel cusp forms of degree two, which are Hecke eigenforms, to central special values of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240912063150983-0859:S0010437X24007267:S0010437X24007267_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$L$</span></span></img></span></span>-functions. The formula is regarded as a natural generalization of the Böcherer conjecture to the non-trivial toroidal character case.</p>","PeriodicalId":55232,"journal":{"name":"Compositio Mathematica","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Compositio Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1112/s0010437x24007267","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

Abstract

We investigate the Gross–Prasad conjecture and its refinement for the Bessel periods in the case of Abstract Image$(\mathrm {SO}(5), \mathrm {SO}(2))$. In particular, by combining several theta correspondences, we prove the Ichino–Ikeda-type formula for any tempered irreducible cuspidal automorphic representation. As a corollary of our formula, we prove an explicit formula relating certain weighted averages of Fourier coefficients of holomorphic Siegel cusp forms of degree two, which are Hecke eigenforms, to central special values of Abstract Image$L$-functions. The formula is regarded as a natural generalization of the Böcherer conjecture to the non-trivial toroidal character case.

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
关于格罗斯-普拉萨德猜想及其对(SO(5), SO(2))的完善和广义伯切尔猜想
我们研究了在 $(\mathrm {SO}(5), \mathrm {SO}(2))$ 的情况下贝塞尔周期的格罗斯-普拉萨德猜想及其细化。特别是,通过结合几种θ对应关系,我们证明了任何回火不可还原尖顶自形表示的伊奇诺-池田式公式。作为我们公式的一个推论,我们证明了一个明确的公式,它将二度全形西格尔凹凸形式(即赫克特征形式)的某些加权平均傅里叶系数与 $L$ 函数的中心特异值联系起来。该公式被视为伯切尔猜想在非三重环状特征情况下的自然推广。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
Compositio Mathematica
Compositio Mathematica 数学-数学
CiteScore
2.10
自引率
0.00%
发文量
62
审稿时长
6-12 weeks
期刊介绍: Compositio Mathematica is a prestigious, well-established journal publishing first-class research papers that traditionally focus on the mainstream of pure mathematics. Compositio Mathematica has a broad scope which includes the fields of algebra, number theory, topology, algebraic and differential geometry and global analysis. Papers on other topics are welcome if they are of broad interest. All contributions are required to meet high standards of quality and originality. The Journal has an international editorial board reflected in the journal content.
期刊最新文献
Cohomological and motivic inclusion–exclusion Improved algebraic fibrings On the Gross–Prasad conjecture with its refinement for (SO(5), SO(2)) and the generalized Böcherer conjecture A Hamiltonian ∐n BO(n)-action, stratified Morse theory and the J-homomorphism The -invariant over splitting fields of Tits algebras
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1