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Linear congruences with ratios


Author: Igor E. Shparlinski
Journal: Proc. Amer. Math. Soc. 144 (2016), 2837-2846
MSC (2010): Primary 11D79, 11L07
DOI: https://doi.org/10.1090/proc/12949
Published electronically: January 20, 2016
MathSciNet review: 3487218
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Abstract: We use new bounds of double exponential sums with ratios of integers from prescribed intervals to get an asymptotic formula for the number of solutions to congruences

$\displaystyle \sum _{j=1}^n a_j \frac {x_j}{y_j} \equiv a_0 \pmod p, $

with variables from rather general sets.

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Additional Information

Igor E. Shparlinski
Affiliation: Department of Pure Mathematics, University of New South Wales, Sydney, New South Wales 2052, Australia
Email: igor.shparlinski@unsw.edu.au

DOI: https://doi.org/10.1090/proc/12949
Keywords: Linear congruences, exponential sums
Received by editor(s): March 26, 2015
Received by editor(s) in revised form: September 4, 2015
Published electronically: January 20, 2016
Additional Notes: This work was supported in part by ARC Grant DP140100118
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2016 American Mathematical Society