Cyclotomic expansions for double twist knots with an odd number of half-twists (2308.16749v1)

Abstract: In this note, we compute the cyclotomic expansion formula for colored Jones polynomial of double twist knots with an odd number of half-twists $\mathcal{K}_{p,\frac{s}{2}}$ by using the Kauffman bracket skein theory. It answers a question proposed by Lovejoy and Osburn in 2019.