Sur les zeros des fonctions L automorphes

Details Sur les zeros des fonctions L automorphes Sur les zeros des fonctions L automorphes

1997-07-31

arxiv.org/abs/math/9707238v1

Mathematics

Number Theory

Scientific paper

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.

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