TY - JOUR

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

AU - Arreche, Carlos E.

AU - Zhang, Yi

N1 - Publisher Copyright:
© 2021 Elsevier Inc.

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 - http://www.scopus.com/inward/record.url?scp=85116054587&partnerID=8YFLogxK

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 -