On some decidable and undecidable problems related to q-difference equations with parameters
Sergei A. Abramov · 2010
We consider linear q-difference equations with polynomial coefficients depending on parameters. For the case when the ground field is Q(q) we propose an algorithm recognizing whether or not there exist numerical values of parameters for which a given equation has a non-zero polynomial solution (alternatively, a rational-function solution). We prove that there exists no such algorithm if the parameter values are polynomials or rational functions of q.