Twisting q-holonomic sequences by complex roots of unity
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We present two new closure properties for q-holonomic sequences, namely twisting by complex roots of unity and raising q to a rational power. The proofs are constructive, work in the multivariate setting of d-finite sequences and are implemented in our Mathematica package HolonomicFunctions. The results are illustrated by twisting natural q-holonomic sequences which appear in quantum topology, namely the colored Jones polynomial of pretzel knots and twist knots. The recurrence of the twisted colored Jones polynomial can be used to compute the asymptotics of the Kashaev invariant of a knot at an arbitrary complex root of unity. This is joint work with Stavros Garoufalidis.