Duke Mathematical Journal

Nonvanishing of L -functions for GL n A Q

Wenzhi Luo

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In this work, we establish new nonvanishing results for automorphic L -functions on GL n A Q . In particular, we show that, given a cuspidal automorphic form π on GL 3 A Q and an arbitrary point s 0 C , there exist infinitely many Dirichlet characters χ with prescribed ramification such that the twisted completed L -functions do not vanish at s 0 : Λ s 0 , π χ 0 .

Article information

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

First available in Project Euclid: 2 June 2005

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

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


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

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