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

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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。

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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).

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