Sur les zeros des fonctions L automorphes
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 KM to obtain a sharp unconditionnal estimate of the (analytic) rank of the new part of J0(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.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.