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

Johannes Middeke

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arXiv · 1705.04188

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

Johannes Middeke

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Abstract

We consider systems A_\ell(t) y(q^\ell 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.

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BibTeX RIS

Johannes Middeke. 2017-05-11. Denominator Bounds and Polynomial Solutions for Systems of q-Recurrences over K(t) for Constant K. https://arxiv.org/abs/1705.04188

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