A theory of residues for skew rational functions
Journal de l’École polytechnique — Mathématiques, Volume 8 (2021), pp. 1159-1192.

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.

Cet article constitue un premier pas en direction du développement de méthodes analytiques pour les polynômes tordus. Précisément, notre principal objectif est de développer une théorie des résidus pour les fractions rationnelles tordues (qui sont, par définition, les quotients de deux polynômes tordus). Nous démontrons en particulier des analogues tordus de la formule des résidus et de la formule classique de changement de variables.

Received:
Accepted:
Published online:
DOI: 10.5802/jep.169
Classification: 16S36,  12E15
Keywords: Residues, skew polynomials
Xavier Caruso 1

1 Université de Bordeaux, Institut Mathématique de Bordeaux (IMB) 351, cours de la Libération, 33405 Talence, France
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Xavier Caruso. A theory of residues for skew rational functions. Journal de l’École polytechnique — Mathématiques, Volume 8 (2021), pp. 1159-1192. doi : 10.5802/jep.169. https://jep.centre-mersenne.org/articles/10.5802/jep.169/

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