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

 

Counting the values taken by algebraic exponential polynomials


Authors: G. R. Everest and I. E. Shparlinski
Journal: Proc. Amer. Math. Soc. 127 (1999), 665-675
MSC (1991): Primary 11B83
MathSciNet review: 1485471
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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
Email: igor@mpce.mq.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04728-0
PII: S 0002-9939(99)04728-0
Received by editor(s): June 20, 1997
Communicated by: David E. Rohrlich
Article copyright: © Copyright 1999 American Mathematical Society