Apparent singularities of linear difference equations with polynomial coefficients

@article{Abramov2005ApparentSO,
  title={Apparent singularities of linear difference equations with polynomial coefficients},
  author={S. Abramov and M. Barkatou and M. V. Hoeij},
  journal={Applicable Algebra in Engineering, Communication and Computing},
  year={2005},
  volume={17},
  pages={117-133}
}
  • S. Abramov, M. Barkatou, M. V. Hoeij
  • Published 2005
  • Computer Science, Mathematics
  • Applicable Algebra in Engineering, Communication and Computing
  • 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 of L such that every singularity of 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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