Estimates for Character Sums and DirichletL-Functions to Smooth Moduli

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 05 Oct 2015Embargo end date: 01 Jan 2015 English Publisher:Oxford University Press (OUP)Journal:International Mathematics Research Notices, volume 2,016, pages 4,602-4,633 (issn: 1073-7928, eissn: 1687-0247,

Copyright policy )Funded by:EC | EQUIARITH

Authors: Irving, A. J.;

doi: 10.1093/imrn/rnv285 , 10.48550/arxiv.1503.07156

arXiv: 1503.07156

Estimates for Character Sums and DirichletL-Functions to Smooth Moduli

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Abstract

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

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

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Mathematics - Number Theory, FOS: Mathematics, Number Theory (math.NT)

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