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Apparent Singularities of Linear Difference Equations with Polynomial Coefficients

S. A. Abramov·M. A. Barkatou·M. van Hoeij
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Abstract

Let L be a linear difference operator with polynomial coefficients. We consider singularities of L that correspond to roots of the trailing (resp. leading) coefficient of L. We prove that one can effectively construct a left multiple with polynomial coefficients L' of L such that every singularity of L' is a singularity of L that is not apparent. As a consequence, if all singularities of L are apparent, then L has a left multiple whose trailing and leading coefficients equal 1.

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S. A. Abramov, M. A. Barkatou, M. van Hoeij. 2004-09-27. Apparent Singularities of Linear Difference Equations with Polynomial Coefficients. https://arxiv.org/abs/math/0409508

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