An elementary bound on Siegel zeroes

JOURNAL OF NUMBER THEORY

卷:212

Article

Morrill, Thomas¹  Trudgian, Tim¹ 

[1] Univ New South Wales, Sch Sci, Canberra, ACT, Australia

关键词: Dirichlet L-functions;    Siegel zeros;    Character sums;   

DOI  :  10.1016/j.jnt.2019.10.024

来源: Elsevier

【 摘 要 】

We consider Dirichlet L-functions L(s, chi) where chi is a real, non-principal character modulo q. Using Pintz's refinement of Page's theorem, we prove that for q >= 3 the function L(s, chi) has at most one real zero beta with 1 - 0.933/log q < beta < 1. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free