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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Character sums over shifted smooth numbers


Author: Igor E. Shparlinski
Journal: Proc. Amer. Math. Soc. 135 (2007), 2699-2705
MSC (2000): Primary 11L40, 11N25
Published electronically: May 2, 2007
MathSciNet review: 2317942
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Abstract | References | Similar Articles | Additional Information

Abstract: We give nontrivial bounds in various ranges for character sums of the form

$\displaystyle \sum_{n\in\mathcal S(x,y)}\chi(n +a), \qquad \gcd(a,p) = 1, $

where $ \chi$ is a nontrivial multiplicative character modulo a prime $ p$ and $ \mathcal S(x,y)$ is the set of positive integers $ n\le x$ that are divisible only by primes $ q \le y$.


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Additional Information

Igor E. Shparlinski
Affiliation: Department of Computing, Macquarie University, Sydney, New South Wales 2109, Australia
Email: igor@ics.mq.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08785-0
PII: S 0002-9939(07)08785-0
Received by editor(s): December 19, 2005
Received by editor(s) in revised form: March 13, 2006, and May 15, 2006
Published electronically: May 2, 2007
Additional Notes: During the preparation of this paper, the author was supported in part by ARC grant DP0556431.
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2007 American Mathematical Society