Meromorphic solutions over \(\mathbb C\) of a system of difference equations with constant coefficients and two recurrent steps (Q1613953)

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.