Average nonvanishing of Dirichlet L-functions atthe central point

Journal article

The Generalized Riemann Hypothesis implies that at least 50% of the central values L(1/2, χ)
are non-vanishing as χ ranges over primitive characters modulo q. We show that one may unconditionally go beyond GRH, in the sense that if one averages over primitive characters modulo q and averages q over an interval, then at least 50.073% of the central values are non-vanishing. The proof utilizes the mollification method with a three-piece mollifier, and relies on estimates for sums of Kloosterman sums due to Deshouillers and Iwaniec.

Authors: Pratt, K

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Mathematical Sciences Publishers
• Journal: Algebra & Number Theory
• Volume: 13
• Issue: 1
• Pages: 227-249
• Publication date: 2019-02-13
• Acceptance date: 2018-09-23
• DOI: 10.2140/ant.2019.13.227
• EISSN: 1944-7833
• ISSN: 1937-0652
• Language: English
• Keywords: central point; mollifier; FFR; nonvanishing; Dirichlet L -function; sums of Kloosterman sums