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 -