Nonvanishing of Dirichlet L-functions

Khan, Rizwanur; Ngo, Hieu

doi:10.2140/ant.2016.10.2081

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Nonvanishing of Dirichlet $L$-functions

Rizwanur Khan and Hieu T. Ngo

Vol. 10 (2016), No. 10, 2081–2091

DOI: 10.2140/ant.2016.10.2081

Abstract

We show that for at least $\frac{3}{8}$ of the primitive Dirichlet characters $χ$ of large prime modulus, the central value $L (\frac{1}{2}, χ)$ does not vanish.

Keywords

$L$-functions, Dirichlet characters, nonvanishing central value, mollifier

Mathematical Subject Classification 2010

Primary: 11M20

Milestones

Received: 13 December 2015

Revised: 18 August 2016

Accepted: 17 September 2016

Published: 9 December 2016

Authors

Rizwanur Khan
Science Program Texas A&M University at Qatar PO Box 23874 Doha Qatar

Hieu T. Ngo
Science Program Texas A&M University at Qatar PO Box 23874 Doha Qatar

Vol. 10, No. 10, 2016