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

DOI:
https://doi.org/10.1090/S0002-9939-99-04728-0

MathSciNet review:
1485471

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Abstract | References | Similar Articles | Additional Information

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 -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:
https://doi.org/10.1090/S0002-9939-99-04728-0

Received by editor(s):
June 20, 1997

Communicated by:
David E. Rohrlich

Article copyright:
© Copyright 1999
American Mathematical Society