THE TWISTED SYMMETRIC SQUARE L-FUNCTION OF GL(r)

被引：31

作者：

Takeda, Shuichiro ^{[1
]}

机构：

[1] Univ Missouri, Dept Math, Columbia, MO 65211 USA

来源：

DUKE MATHEMATICAL JOURNAL | 2014年 / 163卷 / 01期

关键词：

P-ADIC GROUPS; REPRESENTATIONS; EXTENSIONS; THEOREM; SERIES; PROOF; FORMS; GLN;

D O I：

10.1215/00127094-2405497

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider the (partial) symmetric square L-function L-s (s, pi, Sym(2) circle plus x) of an irreducible cuspidal automorphic representation pi of GL(r) (A) twisted by a Hecke character x. In particular, we will show that the L-function L-s (s, pi, Sym(2) circle plus x) is holomorphic for the region Re(s) > 1 - 1/r with the exception that, if X-r omega 2 = 1, a pole might occur at s = 1, where w is the central character of pi. Our method of proof is essentially a (nontrivial) modification of the one by Bump and Ginzburg in which they considered the case x = 1.

引用

页码：175 / 266

页数：92

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