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arXiv · 1705.00280

Denominator Bounds for Systems of Recurrence Equations using $\Pi\Sigma$-Extensions

Johannes Middeke·Carsten Schneider
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Abstract

We consider linear systems of recurrence equations whose coefficients are given in terms of indefinite nested sums and products covering, e.g., the harmonic numbers, hypergeometric products, $q$-hypergeometric products or their mixed versions. These linear systems are formulated in the setting of $\Pi\Sigma$-extensions and our goal is to find a denominator bound (also known as universal denominator) for the solutions; i.e., a non-zero polynomial $d$ such that the denominator of every solution of the system divides $d$. This is the first step in computing all rational solutions of such a rather general recurrence system. Once the denominator bound is known, the problem of solving for rational solutions is reduced to the problem of solving for polynomial solutions.

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Johannes Middeke, Carsten Schneider. 2017-04-30. Denominator Bounds for Systems of Recurrence Equations using $\Pi\Sigma$-Extensions. https://arxiv.org/abs/1705.00280

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