Duke Mathematical Journal

The twisted symmetric square L-function of GL(r)

Shuichiro Takeda

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Abstract

In this paper, we consider the (partial) symmetric square L-function LS(s,π,Sym2χ) of an irreducible cuspidal automorphic representation π of GLr(A) twisted by a Hecke character χ. In particular, we will show that the L-function LS(s,π,Sym2χ) is holomorphic for the region Re(s)>11/r with the exception that, if χrω2=1, a pole might occur at s=1, where ω is the central character of π. Our method of proof is essentially a (nontrivial) modification of the one by Bump and Ginzburg in which they considered the case χ=1.

Article information

Source
Duke Math. J., Volume 163, Number 1 (2014), 175-266.

Dates
First available in Project Euclid: 8 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1389190327

Digital Object Identifier
doi:10.1215/00127094-2405497

Mathematical Reviews number (MathSciNet)
MR3161314

Zentralblatt MATH identifier
1316.11037

Subjects
Primary: 11F66: Langlands $L$-functions; one variable Dirichlet series and functional equations

Citation

Takeda, Shuichiro. The twisted symmetric square $L$ -function of $\operatorname {GL}(r)$. Duke Math. J. 163 (2014), no. 1, 175--266. doi:10.1215/00127094-2405497. https://projecteuclid.org/euclid.dmj/1389190327


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