Denominator Bounds and Polynomial Solutions for Systems of q-Recurrences over K(t) for Constant K
Johannes Middeke · 2017
We consider systems Al(t) y(ql t) + ... + A0(t) y(t) = b(t) of higher order q-recurrence equations with rational coefficients. We extend a method for finding a bound on the maximal power of t in the denominator of arbitrary rational solutions y(t) as well as a method for bounding the degree of polynomial solutions from the scalar case to the systems case. The approach is direct and does not rely on uncoupling or reduction to a first order system. Unlike in the scalar case this usually requires an initial transformation of the system.