Character sums over shifted smooth numbers
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- by Igor E. Shparlinski PDF
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Abstract:
We give nontrivial bounds in various ranges for character sums of the form \[ \sum _{n\in \mathcal S(x,y)}\chi (n +a), \qquad \gcd (a,p) = 1, \] 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 $q \le y$.References
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Additional Information
- Igor E. Shparlinski
- Affiliation: Department of Computing, Macquarie University, Sydney, New South Wales 2109, Australia
- MR Author ID: 192194
- Email: igor@ics.mq.edu.au
- 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
- © Copyright 2007 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 2699-2705
- MSC (2000): Primary 11L40, 11N25
- DOI: https://doi.org/10.1090/S0002-9939-07-08785-0
- MathSciNet review: 2317942