Rationality for isobaric automorphic representations: the CM-case.

IF 0.8 4区数学 Q2 MATHEMATICS

Monatshefte fur Mathematik 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

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 $L (s, Π \times Π^{'})$ (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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等边自动表征的合理性：CM 案例。

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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来源期刊

Monatshefte fur Mathematik 数学-数学

CiteScore

1.60

自引率

11.10%

发文量

155

审稿时长

4-8 weeks

期刊介绍： The journal was founded in 1890 by G. v. Escherich and E. Weyr as "Monatshefte für Mathematik und Physik" and appeared with this title until 1944. Continued from 1948 on as "Monatshefte für Mathematik", its managing editors were L. Gegenbauer, F. Mertens, W. Wirtinger, H. Hahn, Ph. Furtwängler, J. Radon, K. Mayrhofer, N. Hofreiter, H. Reiter, K. Sigmund, J. Cigler. The journal is devoted to research in mathematics in its broadest sense. Over the years, it has attracted a remarkable cast of authors, ranging from G. Peano, and A. Tauber to P. Erdös and B. L. van der Waerden. The volumes of the Monatshefte contain historical achievements in analysis (L. Bieberbach, H. Hahn, E. Helly, R. Nevanlinna, J. Radon, F. Riesz, W. Wirtinger), topology (K. Menger, K. Kuratowski, L. Vietoris, K. Reidemeister), and number theory (F. Mertens, Ph. Furtwängler, E. Hlawka, E. Landau). It also published landmark contributions by physicists such as M. Planck and W. Heisenberg and by philosophers such as R. Carnap and F. Waismann. In particular, the journal played a seminal role in analyzing the foundations of mathematics (L. E. J. Brouwer, A. Tarski and K. Gödel). The journal publishes research papers of general interest in all areas of mathematics. Surveys of significant developments in the fields of pure and applied mathematics and mathematical physics may be occasionally included.