Two theorems of the non-vanishing of special values of L functions

Citation
E. Kowalski et P. Michel, Two theorems of the non-vanishing of special values of L functions, MANUSC MATH, 104(1), 2001, pp. 1-19
Citations number
22
Language
FRANCESE
art.tipo
Article
Categorie Soggetti
Mathematics
Journal title
MANUSCRIPTA MATHEMATICA
ISSN journal
0025-2611 → ACNP
Volume
104
Issue
1
Year of publication
2001
Pages
1 - 19
Database
ISI
SICI code
0025-2611(200101)104:1<1:TTOTNO>2.0.ZU;2-S
Abstract
In answer to questions recently raised by Merel [Mer], we prove two non-van ishing theorems for the central value of automorphic L-functions: let p be prime and let chi be a primitive character module p. Then for all p large e nough 1. If chi is not quadratic and even, there exists a primitive weight 2 form f of level p with L(f x chi, 1/2) not equal 0. 2. If chi is quadratic and even, then there exists a primitive weight 2 for m f of level p with ord (s=1/2) L(f,s)L(f x chi ,s) = 1.