Entire solutions of a system of difference equations
type: Item
instance of: scholarly article
title: Entire solutions of a system of difference equations
zbMATH Open document ID: 0796.39006
publication date: 1994-09-26T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/75020
review text: In answer to a question of \textit{D. W. Masser} [Prog. Math. 31, 173-190 (1983; Zbl 0549.32002)] we prove that, for almost all systems of difference equations \(\sum_{0 \leq m \leq M} A_ m (z) f(z+\alpha m) = \sum_{0 \leq n \leq N} B_ n(z) f(z+ \beta n)=0\), where \(A_ m\) and \(B_ n\) are polynomials and \(\alpha, \beta \in \mathbb{C}^*\) are \(\mathbb{R}\)- linearly independant, any solution \(f\) which is an entire function is the quotient of an exponential polynomial by a polynomial. We give a similar result when the second relation is replaced by a differential equation \(\sum_{0 \leq n \leq N} B_ n (z)f^{(n)} (z)=0\).
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 30D05
Mathematics Subject Classification ID: 39B32
zbMATH DE Number: 490694
zbMATH Keywords: entire solutions
zbMATH Keywords: systems of difference equations
author: J.-P. Bézivin
author: François Gramain
MaRDI profile type: Publication
OpenAlex ID: W2026379968
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DOI: 10.5802/AIF.1356
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 490694