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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- G. R. Everest
- Affiliation: School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, Norfolk, United Kingdom
- Email: firstname.lastname@example.org
- I. E. Shparlinski
- Affiliation: School of MPCE, Macquarie University, New South Wales 2109, Australia
- MR Author ID: 192194
- Email: email@example.com
- 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