Counting the values taken by algebraic exponential polynomials

G. R. Everest*, I. E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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 5-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.

Original languageEnglish
Pages (from-to)665-675
Number of pages11
JournalProceedings of the American Mathematical Society
Issue number3
Publication statusPublished - 1999


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