Computing differential Galois groups of second-order linear q-difference equations

Carlos E. Arreche; Yi Zhang

doi:10.1016/j.aam.2021.102273

Computing differential Galois groups of second-order linear q-difference equations

Carlos E. Arreche
, Yi Zhang^*

^*Corresponding author for this work

Department of Applied Mathematics

University of Texas at Dallas

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

We apply the differential Galois theory for difference equations developed by Hardouin and Singer to compute the differential Galois group for a second-order linear q-difference equation with rational function coefficients. This Galois group encodes the possible polynomial differential relations among the solutions of the equation. We apply our results to compute the differential Galois groups of several concrete q-difference equations, including for the colored Jones polynomial of a certain knot.

Original language	English
Article number	102273
Journal	Advances in Applied Mathematics
Volume	132
DOIs	https://doi.org/10.1016/j.aam.2021.102273
Publication status	Published - Jan 2022

Keywords

Difference Galois theory
Differential Galois theory
q-Difference equations

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10.1016/j.aam.2021.102273

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title = "Computing differential Galois groups of second-order linear q-difference equations",

abstract = "We apply the differential Galois theory for difference equations developed by Hardouin and Singer to compute the differential Galois group for a second-order linear q-difference equation with rational function coefficients. This Galois group encodes the possible polynomial differential relations among the solutions of the equation. We apply our results to compute the differential Galois groups of several concrete q-difference equations, including for the colored Jones polynomial of a certain knot.",

keywords = "Difference Galois theory, Differential Galois theory, q-Difference equations",

author = "Arreche, \{Carlos E.\} and Yi Zhang",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

year = "2022",

month = jan,

doi = "10.1016/j.aam.2021.102273",

language = "English",

volume = "132",

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T1 - Computing differential Galois groups of second-order linear q-difference equations

AU - Arreche, Carlos E.

AU - Zhang, Yi

PY - 2022/1

Y1 - 2022/1

N2 - We apply the differential Galois theory for difference equations developed by Hardouin and Singer to compute the differential Galois group for a second-order linear q-difference equation with rational function coefficients. This Galois group encodes the possible polynomial differential relations among the solutions of the equation. We apply our results to compute the differential Galois groups of several concrete q-difference equations, including for the colored Jones polynomial of a certain knot.

AB - We apply the differential Galois theory for difference equations developed by Hardouin and Singer to compute the differential Galois group for a second-order linear q-difference equation with rational function coefficients. This Galois group encodes the possible polynomial differential relations among the solutions of the equation. We apply our results to compute the differential Galois groups of several concrete q-difference equations, including for the colored Jones polynomial of a certain knot.

KW - Difference Galois theory

KW - Differential Galois theory

KW - q-Difference equations

UR - https://www.scopus.com/pages/publications/85116054587

U2 - 10.1016/j.aam.2021.102273

DO - 10.1016/j.aam.2021.102273

M3 - Article

AN - SCOPUS:85116054587

SN - 0196-8858

VL - 132

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

M1 - 102273

ER -

Computing differential Galois groups of second-order linear q-difference equations

Abstract

Keywords

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