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.
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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@article{JEP_2021__8__1159_0,
author = {Xavier Caruso},
title = {A theory of residues for skew~rational~functions},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {1159--1192},
publisher = {\'Ecole polytechnique},
volume = {8},
year = {2021},
doi = {10.5802/jep.169},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.169/}
}
TY - JOUR AU - Xavier Caruso TI - A theory of residues for skew rational functions JO - Journal de l’École polytechnique — Mathématiques PY - 2021 SP - 1159 EP - 1192 VL - 8 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.169/ DO - 10.5802/jep.169 LA - en ID - JEP_2021__8__1159_0 ER -
Xavier Caruso. A theory of residues for skew rational functions. Journal de l’École polytechnique — Mathématiques, Tome 8 (2021), pp. 1159-1192. doi : 10.5802/jep.169. https://jep.centre-mersenne.org/articles/10.5802/jep.169/
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