等边自动表征的合理性：CM 案例。

Pub Date : 2018-01-01 Epub Date: 2018-05-21 DOI:10.1007/s00605-018-1188-5

Harald Grobner

{"title":"等边自动表征的合理性：CM 案例。","authors":"Harald Grobner","doi":"10.1007/s00605-018-1188-5","DOIUrl":null,"url":null,"abstract":"In this note we prove a simultaneous extension of the author's joint result with M. Harris for critical values of Rankin-Selberg L-functions <math><mrow><mi>L</mi> <mo>(</mo> <mi>s</mi> <mo>,</mo> <mi>Π</mi> <mo>×</mo> <msup><mi>Π</mi> <mo>'</mo></msup> <mo>)</mo></mrow> </math> (Grobner and Harris in J Inst Math Jussieu 15:711-769, 2016, Thm. 3.9) to (i) general CM-fields F and (ii) cohomological automorphic representations <math> <mrow><msup><mi>Π</mi> <mo>'</mo></msup> <mo>=</mo> <msub><mi>Π</mi> <mn>1</mn></msub> <mo>⊞</mo> <mo>⋯</mo> <mo>⊞</mo> <msub><mi>Π</mi> <mi>k</mi></msub> </mrow> </math> which are the isobaric sum of unitary cuspidal automorphic representations <math><msub><mi>Π</mi> <mi>i</mi></msub> </math> of general linear groups of arbitrary rank over F. In this sense, the main result of these notes, cf. Theorem 1.9, is a generalization, as well as a complement, of the main results in Raghuram (Forum Math 28:457-489, 2016; Int Math Res Not 2:334-372, 2010. https://doi.org/10.1093/imrn/rnp127), and Mahnkopf (J Inst Math Jussieu 4:553-637, 2005).","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6428343/pdf/","citationCount":"0","resultStr":"{\"title\":\"Rationality for isobaric automorphic representations: the CM-case.\",\"authors\":\"Harald Grobner\",\"doi\":\"10.1007/s00605-018-1188-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this note we prove a simultaneous extension of the author's joint result with M. Harris for critical values of Rankin-Selberg L-functions <math><mrow><mi>L</mi> <mo>(</mo> <mi>s</mi> <mo>,</mo> <mi>Π</mi> <mo>×</mo> <msup><mi>Π</mi> <mo>'</mo></msup> <mo>)</mo></mrow> </math> (Grobner and Harris in J Inst Math Jussieu 15:711-769, 2016, Thm. 3.9) to (i) general CM-fields F and (ii) cohomological automorphic representations <math> <mrow><msup><mi>Π</mi> <mo>'</mo></msup> <mo>=</mo> <msub><mi>Π</mi> <mn>1</mn></msub> <mo>⊞</mo> <mo>⋯</mo> <mo>⊞</mo> <msub><mi>Π</mi> <mi>k</mi></msub> </mrow> </math> which are the isobaric sum of unitary cuspidal automorphic representations <math><msub><mi>Π</mi> <mi>i</mi></msub> </math> of general linear groups of arbitrary rank over F. In this sense, the main result of these notes, cf. Theorem 1.9, is a generalization, as well as a complement, of the main results in Raghuram (Forum Math 28:457-489, 2016; Int Math Res Not 2:334-372, 2010. https://doi.org/10.1093/imrn/rnp127), and Mahnkopf (J Inst Math Jussieu 4:553-637, 2005).\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2018-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6428343/pdf/\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00605-018-1188-5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2018/5/21 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00605-018-1188-5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2018/5/21 0:00:00","PubModel":"Epub","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

在本注释中，我们同时证明了作者与 M. Harris 针对 Rankin-Selberg L 函数 L ( s , Π × Π ' ) 临界值的联合结果（Grobner 和 Harris 在 J Inst Math Jussieu 15:711-769, 2016, Thm.9）到（i）一般 CM 场 F 和（ii）同调自形表示 Π ' = Π 1 ⋯ ⊞ Π k，它们是 F 上任意秩的一般线性群的单元簇自形表示 Π i 的等价和。从这个意义上说，这些注释的主要结果，参见定理 1.9，是对 Raghuram (Forum Math 28:457-489, 2016; Int Math Res Not 2:334-372, 2010. https://doi.org/10.1093/imrn/rnp127) 和 Mahnkopf (J Inst Math Jussieu 4:553-637, 2005) 中主要结果的概括和补充。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

Rationality for isobaric automorphic representations: the CM-case.

In this note we prove a simultaneous extension of the author's joint result with M. Harris for critical values of Rankin-Selberg L-functions $L (s, Π \times Π^{'})$ (Grobner and Harris in J Inst Math Jussieu 15:711-769, 2016, Thm. 3.9) to (i) general CM-fields F and (ii) cohomological automorphic representations $Π^{'} = Π_{1} ⊞ \dots ⊞ Π_{k}$ which are the isobaric sum of unitary cuspidal automorphic representations $Π_{i}$ of general linear groups of arbitrary rank over F. In this sense, the main result of these notes, cf. Theorem 1.9, is a generalization, as well as a complement, of the main results in Raghuram (Forum Math 28:457-489, 2016; Int Math Res Not 2:334-372, 2010. https://doi.org/10.1093/imrn/rnp127), and Mahnkopf (J Inst Math Jussieu 4:553-637, 2005).

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助