Équations exponentielles polynômes et suites récurrentes linéaires. (Exponential polynomial equations and linear recurrence sequences). (French) Zbl 0621.10014

Laurent, Michel

Journées arithmétiques, Besançon/France 1985, Astérisque 147/148, 121-139 (1987).

[For the entire collection see Zbl 0605.00004.]
The main result of this paper is that common zeros in \({\mathbb{Z}}^ r\) of a finite family of exponential-polynomial functions (with complex coefficients) lie ”near” affine subgroups explicitly given (they belong to such subgroups if only exponential functions are involved). Applications to algebraic equations relating values of linear recurrence sequences are given. Unfortunately the proofs, based on a theorem of Schlickewei are not effective.

Reviewer: G.Christol

MSC:

11D61	Exponential Diophantine equations
11B37	Recurrences

Keywords:

common zeros; exponential-polynomial functions; affine subgroups; values of linear recurrence sequences