English

Negative values of truncations to $L(1,\chi)$

Number Theory 2007-05-23 v1

Abstract

For a given xx we consider the minimum of nxχ(n)/n\sum_{n\le x} \chi(n)/n as χ\chi ranges over all quadratic Dirichlet characters. For all large xx, this minimum is negative and we give upper and lower bounds for it.

Keywords

Cite

@article{arxiv.math/0508361,
  title  = {Negative values of truncations to $L(1,\chi)$},
  author = {Andrew Granville and K. Soundararajan},
  journal= {arXiv preprint arXiv:math/0508361},
  year   = {2007}
}

Comments

8 pages

R2 v1 2026-07-22T17:23:16.307Z