1. Lower bounds for L -functions at the edge of the critical strip
- Author
-
Stephen Gelbart and Erez Lapid
- Subjects
Conjecture ,Mathematics::Number Theory ,General Mathematics ,Automorphic form ,Type (model theory) ,Automorphic function ,Upper and lower bounds ,Combinatorics ,Algebra ,symbols.namesake ,Langlands–Shahidi method ,Eisenstein series ,symbols ,L-function ,Mathematics::Representation Theory ,Mathematics - 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 Vallee 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.
- Published
- 2006
- Full Text
- View/download PDF