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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Counting the values taken by algebraic exponential polynomials
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by G. R. Everest and I. E. Shparlinski PDF
Proc. Amer. Math. Soc. 127 (1999), 665-675 Request permission

Abstract:

We prove an effective mean-value theorem for the values of a non-degenerate, algebraic exponential polynomial in several variables. These objects generalise simultaneously the fundamental examples of linear recurrence sequences and sums of $S$-units. The proof is based on an effective, uniform estimate for the deviation of the exponential polynomial from its expected value. This estimate is also used to obtain a non-effective asymptotic formula counting the norms of these values below a fixed bound.
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Additional Information
  • G. R. Everest
  • Affiliation: School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, Norfolk, United Kingdom
  • Email: g.everest@uea.ac.uk
  • I. E. Shparlinski
  • Affiliation: School of MPCE, Macquarie University, New South Wales 2109, Australia
  • MR Author ID: 192194
  • Email: igor@mpce.mq.edu.au
  • Received by editor(s): June 20, 1997
  • Communicated by: David E. Rohrlich
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 665-675
  • MSC (1991): Primary 11B83
  • DOI: https://doi.org/10.1090/S0002-9939-99-04728-0
  • MathSciNet review: 1485471