Non annulation des fonctions L automorphes au point central

Details Non annulation des fonctions L automorphes au point central Non annulation des fonctions L automorphes au point central

2008-12-30

arxiv.org/abs/0812.5093v1

Mathematics

Number Theory

29 p

Scientific paper

The question about modular forms have recently received a lot of attention; concerning the non-vanishing of automorphic L-functions Michel, Kowalski and Vanderkam proved (among others results) that there's positive proportion of non-vanishing of primitives forms at the critical point. This result was proved by these authors in the prime level case; on the othe hand, Iwaniec, Luo and Sarnak showed the same result for the squarefree level case. In order to understand the influence of the arithmetic shape of level forms in their vanishing, this paper studies a generalisation to the primitives forms with prime powers level.

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