Browsing by Author "Lovejoy, Jeremy"
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- ItemThe colored Jones polynomial and Kontsevich-Zagier series for double twist knots(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2017) Lovejoy, Jeremy; Osburn, RobertUsing a result of Takata, we prove a formula for the colored Jones polynomial of the double twist knots K(−m,−p) and K(−m,p) where m and p are positive integers. In the (−m,−p) case, this leads to new families of q-hypergeometric series generalizing the Kontsevich-Zagier series. Comparing with the cyclotomic expansion of the colored Jones polynomials of K(m,p) gives a generalization of a duality at roots of unity between the Kontsevich-Zagier function and the generating function for strongly unimodal sequences.