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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Linear congruences with ratios
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by Igor E. Shparlinski PDF
Proc. Amer. Math. Soc. 144 (2016), 2837-2846 Request permission

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 \[ \sum _{j=1}^n a_j \frac {x_j}{y_j} \equiv a_0 \pmod p, \] 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
  • MR Author ID: 192194
  • Email: igor.shparlinski@unsw.edu.au
  • 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
  • © Copyright 2016 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 2837-2846
  • MSC (2010): Primary 11D79, 11L07
  • DOI: https://doi.org/10.1090/proc/12949
  • MathSciNet review: 3487218