Counting the values taken by algebraic exponential polynomials
Authors:
G. R. Everest and I. E. Shparlinski
Journal:
Proc. Amer. Math. Soc. 127 (1999), 665675
MSC (1991):
Primary 11B83
MathSciNet review:
1485471
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Abstract: We prove an effective meanvalue theorem for the values of a nondegenerate, 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 noneffective asymptotic formula counting the norms of these values below a fixed bound.
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 I. Shparlinski, On the number of distinct prime divisors of recurrence sequences, Matem. Zametki 42 (1987), 494507 (Russian).
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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/S0002993999047280
PII:
S 00029939(99)047280
Received by editor(s):
June 20, 1997
Communicated by:
David E. Rohrlich
Article copyright:
© Copyright 1999
American Mathematical Society
