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arXiv:1403.7079 [math.NT]AbstractReferencesReviewsResources

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

Daniel Fiorilli

Published 2014-03-27Version 1

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 $L(\frac 12,\chi)=0$.

Comments: 11 pages
Categories: math.NT
Subjects: 11M20, 11M26, 11N13
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