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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna


IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2017: 0.67

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1435-5337
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Volume 27, Issue 5

Issues

Character sums over unions of intervals

Xuancheng Shao
Published Online: 2014-01-10 | DOI: https://doi.org/10.1515/forum-2013-0080

Abstract

Let q be a cube-free positive integer and χ(modq) be a non-principal Dirichlet character. Our main result is a Burgess-type estimate for nAχ(n), where A[1,q] is the union of s disjoint intervals I1,...,Is. We obtain a nontrivial estimate for the character sum over A whenever |A|s-1/2>q1/4+ϵ and each interval Ij (1js) has length |Ij|>qϵ for any ϵ>0. This follows from an improvement of a mean value Burgess-type estimate studied by Heath-Brown [Number Theory and Related Fields, Springer Proc. Math. Statist. 43, New York (2013), 199–213].

Keywords: Character sum; harmonic analysis

MSC: 11L40

About the article

Received: 2013-05-16

Revised: 2013-10-24

Published Online: 2014-01-10

Published in Print: 2015-09-01


Citation Information: Forum Mathematicum, Volume 27, Issue 5, Pages 3017–3026, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2013-0080.

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