Differential transcendence criteria for second-order linear difference equations and elliptic hypergeometric functions

Arreche, Carlos E.; Dreyfus, Thomas; Roques, Julien

doi:10.5802/jep.143

Journal De L’École Polytechnique — Mathématiques

2021

DOI: 10.5802/jep.143

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Differential transcendence criteria for second-order linear difference equations and elliptic hypergeometric functions

Carlos E. Arreche¹,

Thomas Dreyfus²,

Julien Roques³

Abstract: Cet article est mis à disposition selon les termes de la licence LICENCE INTERNATIONALE D'ATTRIBUTION CREATIVE COMMONS BY 4.0.

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2024

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Cited by 2 publications

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Almost-simple affine difference algebraic groups

Wibmer

2021

Math. Z.

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Affine difference algebraic groups are a generalization of affine algebraic groups obtained by replacing algebraic equations with algebraic difference equations. We show that the isomorphism theorems from abstract group theory have meaningful analogs for these groups and we establish a Jordan-Hölder type theorem that allows us to decompose any affine difference algebraic group into almost-simple affine difference algebraic groups. We also characterize almost-simple affine difference algebraic groups via almost-simple affine algebraic groups.

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Almost-simple affine difference algebraic groups

Wibmer

2021

Math. Z.

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Twisted Mahler Discrete Residues

Arreche,

Zhang

2024

International Mathematics Research Notices

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Recently we constructed Mahler discrete residues for rational functions and showed they comprise a complete obstruction to the Mahler summability problem of deciding whether a given rational function $f(x)$ is of the form $g(x^{p})-g(x)$ for some rational function $g(x)$ and an integer $p> 1$. Here we develop a notion of $\lambda $-twisted Mahler discrete residues for $\lambda \in \mathbb{Z}$, and show that they similarly comprise a complete obstruction to the twisted Mahler summability problem of deciding whether a given rational function $f(x)$ is of the form $p^{\lambda } g(x^{p})-g(x)$ for some rational function $g(x)$ and an integer $p>1$. We provide some initial applications of twisted Mahler discrete residues to differential creative telescoping problems for Mahler functions and to the differential Galois theory of linear Mahler equations.

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Differential transcendence criteria for second-order linear difference equations and elliptic hypergeometric functions

Abstract: Cet article est mis à disposition selon les termes de la licence LICENCE INTERNATIONALE D'ATTRIBUTION CREATIVE COMMONS BY 4.0.

Cited by 2 publications

References 22 publications

Almost-simple affine difference algebraic groups

Almost-simple affine difference algebraic groups

Twisted Mahler Discrete Residues

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