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A theory of residues for skew rational functions

Xavier Caruso 1, 2
2 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : This paper constitutes a first attempt to do analysis with skew polynomials. Precisely, our main objective is to develop a theory of residues for skew rational functions (which are, by definition, the quotients of two skew polynomials). We prove in particular a skew analogue of the residue formula and a skew analogue of the classical formula of change of variables for residues.
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Submitted on : Wednesday, June 16, 2021 - 9:24:02 PM
Last modification on : Saturday, December 4, 2021 - 3:43:55 AM

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  • HAL Id : hal-02268790, version 2
  • ARXIV : 1908.08430

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Xavier Caruso. A theory of residues for skew rational functions. Journal de l'École polytechnique — Mathématiques, École polytechnique, 2021, 8, pp.1159-1192. ⟨hal-02268790v2⟩

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