Apparent Singularities of Linear Difference Equations with Polynomial Coefficients

2004/09/27 by S. A. Abramov, С. А. Абрамов, Abramov, S. A. +5
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Meromorphic and Entire Functions #Polynomial and algebraic computation #math.CA

paper · pdf · doi:10.48550/arxiv.math/0409508

arxiv created 2004/09/27 · openalex publication_date 2004/09/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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