On the non-vanishing of Dirichlet L-functions at the central point

2014/03/27 by Fiorilli, Daniel
#11M20 (primary) #11M26 #11N13 (secondary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1403.7079

Abstract

We investigate the consequences of natural conjectures of Montgomery type on the non-vanishing of Dirichlet L-functions at the central point. We first justify these conjectures using probabilistic arguments. We then show using a result of Bombieri, Friedlander and Iwaniec and a result of the author that they imply that almost all Dirichlet L-functions do not vanish at the central point. We also deduce a quantitative upper bound for the proportion of Dirichlet L-functions for which L(\frac 12,χ)=0.

Related

• Non-vanishing of Dirichlet L-functions at the Central Point
• Vanishing of Dirichlet L-functions at the central point over function fields
• Large values of quadratic Dirichlet L-functions near the central point
• Non-vanishing of Cubic Dirichlet L-Functions over the Eisenstein Field
• Conditional estimates on the argument of Dirichlet L-functions with applications to low-lying zeros