Duke Mathematical Journal

Nonvanishing of $L$-functions for $\GL(n, \mathbf{A}_Q)$

Wenzhi Luo

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Abstract

In this work, we establish new nonvanishing results for automorphic $L$-functions on $\GL(n, \mathbf{A}_Q)$. In particular, we show that, given a cuspidal automorphic form $\pi$ on $\GL(3, \mathbf{A}_Q)$ and an arbitrary point $s_{0} \in {\bf C}$, there exist infinitely many Dirichlet characters $\chi$ with prescribed ramification such that the twisted completed $L$-functions do not vanish at $s_{0}$: $\Lambda (s_{0}, \pi \otimes \chi) \neq 0$.

Article information

Source
Duke Math. J. Volume 128, Number 2 (2005), 199-207.

Dates
First available in Project Euclid: 2 June 2005

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1117728415

Digital Object Identifier
doi:10.1215/S0012-7094-04-12821-0

Mathematical Reviews number (MathSciNet)
MR2140263

Zentralblatt MATH identifier
02201101

Subjects
Primary: 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols
Secondary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields

Citation

Luo, Wenzhi. Nonvanishing of L -functions for GL n A Q . Duke Math. J. 128 (2005), no. 2, 199--207. doi:10.1215/S0012-7094-04-12821-0. http://projecteuclid.org/euclid.dmj/1117728415.


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