Denominator Bounds and Polynomial Solutions for Systems of q-Recurrences over K(t) for Constant K

05/11/2017

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by   Johannes Middeke, et al.

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We consider systems A_ℓ(t) y(q^ℓ t) + ... + A_0(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.