Vol. 10, No. 10, 2016

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Nonvanishing of Dirichlet $L$-functions

Rizwanur Khan and Hieu T. Ngo

Vol. 10 (2016), No. 10, 2081–2091
Abstract

We show that for at least 3 8 of the primitive Dirichlet characters χ of large prime modulus, the central value L(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