Character sums over shifted smooth numbers

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Abstract

We give nontrivial bounds in various ranges for character sums of the form Σc∈S(x,y) χ(n+a), gcd(a,p) = 1, where χ is a nontrivial multiplicative character modulo a prime p and S(x,y) is the set of positive integers n ≤ x that are divisible only by primes q ≤ y.

Original languageEnglish
Pages (from-to)2699-2705
Number of pages7
JournalProceedings of the American Mathematical Society
Volume135
Issue number9
DOIs
Publication statusPublished - Sep 2007

Bibliographical note

Copyright 2007 American Mathematical Society. First published in Proceedings of the American Mathematical Society, Volume 135, Issue 9, pp. 2699-2705, published by the American Mathematical Society. The original article can be found at http://dx.doi.org/10.1090/S0002-9939-07-08785-0.

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