Sur les zeros des fonctions L automorphes
Number Theory
2008-02-03 v1
Abstract
We study, on average over f, zeros of the L-functions of primitive weight two forms of level q (fixed). We prove, on the one hand, density theorems for the zeros (similar to the results of Bombieri, Jutila, Motohashi, Selberg in the case of characters), which are applied in \cite{KM} to obtain a sharp unconditionnal estimate of the (analytic) rank of the new part of J_0(q); and, on the other hand, non-vanishing theorems at the critical point, showing that a positive proportion of L-functions are non zero there.
Cite
@article{arxiv.math/9707238,
title = {Sur les zeros des fonctions L automorphes},
author = {Emmanuel Kowalski and Philippe Michel},
journal= {arXiv preprint arXiv:math/9707238},
year = {2008}
}