Denominator Bounds for Systems of Recurrence Equations using ΠΣ-Extensions

04/30/2017

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by   Johannes Middeke, et al.

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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 ΠΣ-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.