2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153145We 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.Number Theorytext