Meromorphic solutions over \(\mathbb C\) of a system of difference equations with constant coefficients and two recurrent steps
type: Item
instance of: scholarly article
title: Meromorphic solutions over \(\mathbb C\) of a system of difference equations with constant coefficients and two recurrent steps
zbMATH Open document ID: 1004.39002
author: Jean-Claude Jolly
publication date: 2002-09-03T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/115988
review text: The author considers meromorphic solutions \(f\) of the simultaneous difference equations \(\sum_{k,l} a_{k,l}\) \(f(z+kw+lw')=0\) and \(\sum_{k,l} b_{k,l} f(z+kw+lw')=0\), where the \(a_{k,l}\) and \(b_{k,l}\) are constants, the sums being finite, and where \(w\) and \(w'\) are non-zero complex numbers with \(Im(w'/w)>0\). The main result is a complete description of the solution space of this system of equations. This description is rather lengthy and thus not included here.
reviewed by: Walter Bergweiler
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 39A70
Mathematics Subject Classification ID: 30D30
Mathematics Subject Classification ID: 30D20
zbMATH DE Number: 1794808
zbMATH Keywords: meromorphic solutions
zbMATH Keywords: simultaneous difference equations
zbMATH Keywords: elliptic function
MaRDI profile type: Publication
OpenAlex ID: W2471756126
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DOI: 10.5802/AIF.1895
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 1794808