@inproceedings{3d507bc4bf5845f9b7b209385c7743f6,
title = "Mahler Discrete Residues and Summability for Rational Functions",
abstract = "We construct Mahler discrete residues for rational functions and show that they comprise a complete obstruction to the Mahler summability problem of deciding whether a given rational function f(x) is of the form g(xP)-g(x) for some rational function g(x) and an integer p > 1. This extends to the Mahler case the analogous notions, properties, and applications of discrete residues (in the shift case) and q-discrete residues (in the q-difference case) developed by Chen and Singer. Along the way we define several additional notions that promise to be useful for addressing related questions involving Mahler difference fields of rational functions, including in particular telescoping problems and problems in the (differential) Galois theory of Mahler difference equations.",
keywords = "creative telescoping, difference equations, difference fields, discrete residues, mahler operator, partial fractions, summability",
author = "Arreche, \{Carlos E.\} and Yi Zhang",
note = "Publisher Copyright: {\textcopyright} 2022 ACM.",
year = "2022",
month = jul,
day = "5",
doi = "10.1145/3476446.3536186",
language = "English",
series = "Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC",
publisher = "Association for Computing Machinery",
pages = "525–533",
editor = "Amir Hashemi",
booktitle = "ISSAC 2022 - Proceedings of the 2022 ACM International Symposium on Symbolic and Algebraic Computation",
}