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Apparent Singularities of Linear Difference Equations with Polynomial Coefficients

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arxiv math/0409508 v1 pith:KI7F5GTG submitted 2004-09-27 math.CA

S. A. Abramov , M. A. Barkatou , M. van Hoeij This is my paper · ORCID
classification math.CA
keywords coefficientsapparentpolynomialsingularitiesdifferenceleadingleftlinear
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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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