## 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.## References

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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