Abstract

We prove a coarse lower bound for L-functions of Langlands-Shahidi type of generic cuspidal automorphic representations on the line Re (s) = 1. We follow the path suggested by Sarnak using Eisenstein series and the Maass-Selberg relations. The bounds are weaker than what the method of de la Vallée Poussin gives for the standard L-functions of GLn, but are applicable to more general automorphic L-functions. Our Theorem answers in a strong form a conjecture posed by Gelbart and Shahidi [J. Amer. Math. Soc. 14 (2001)], and sharpens and considerably simplifies the proof of the main result of that paper.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 619-638
Launched on MUSE
2006-05-24
Open Access
No
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