Estimates for character sums and Dirichlet $L$-functions to smooth moduli

A. J. Irving

Estimates for character sums and Dirichlet $L$-functions to smooth moduli

Number Theory 2015-03-25 v1

Authors: A. J. Irving

Abstract

We use the $q$ -analogue of van der Corput's method to estimate short character sums to smooth moduli. If $\chi$ is a primitive Dirichlet character modulo a squarefree, $q^\delta$ -smooth integer $q$ we show that $L(\frac12,\chi)\ll_\epsilon q^{\frac{27}{164}+O(\delta)+\epsilon}.$

Keywords

dirichlet characters

Cite

@article{arxiv.1503.07156,
  title  = {Estimates for character sums and Dirichlet $L$-functions to smooth moduli},
  author = {A. J. Irving},
  journal= {arXiv preprint arXiv:1503.07156},
  year   = {2015}
}

Comments

27 pages, including a 4 page appendix by \'e. Fouvry, E. Kowalski and P. Michel

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