English

An explicit upper bound for $L(1, \chi)$ when $\chi$ is quadratic

Number Theory 2023-03-27 v1

Abstract

We consider Dirichlet LL-functions L(s,χ)L(s, \chi) where χ\chi is a non-principal quadratic character to the modulus qq. We make explicit a result due to Pintz and Stephens by showing that L(1,χ)12logq|L(1, \chi)|\leq \frac{1}{2}\log q for all q21023q\geq 2\cdot 10^{23} and L(1,χ)920logq|L(1, \chi)|\leq \frac{9}{20}\log q for all q51050q\geq 5\cdot 10^{50}.

Keywords

Cite

@article{arxiv.2303.13785,
  title  = {An explicit upper bound for $L(1, \chi)$ when $\chi$ is quadratic},
  author = {D. R. Johnston and O. Ramare and T. S. Trudgian},
  journal= {arXiv preprint arXiv:2303.13785},
  year   = {2023}
}

Comments

17 pages

R2 v1 2026-06-28T09:31:32.274Z