A theory of residues for skew rational functions

Xavier Caruso (1, 2)

1 IMB - Institut de Mathématiques de Bordeaux
2 LFANT - Lithe and fast algorithmic number theory

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.

Domaines: Anneaux et algèbres [math.RA]; Théorie de l'information et codage [math.IT]; Calcul formel [cs.SC]

Xavier Caruso. A theory of residues for skew rational functions. Journal de l'École polytechnique — Mathématiques, 2021, 8, pp.1159-1192. ⟨10.5802/jep.169⟩. ⟨hal-02268790v2⟩