Moments and zero density estimates for Dirichlet L-functions

Abstract

In this paper, we estimate the density of zeros of primitive Dirichlet L-functions in the half-plane ℜ(s) > 1/2, under the assumption of a plausible conjecture on high moments of Dirichlet L-functions on the critical line. We conditionally improve the results of Huxley [9], Jutila [13], Heath-Brown [5, 6] and Bourgain [1]