Torus knots and quantum modular forms

Kazuhiro Hikami, Jeremy Lovejoy

    Research output: Contribution to journalArticlepeer-review

    26 Citations (Scopus)


    In this paper we compute a q-hypergeometric expression for the cyclotomic expansion of the colored Jones polynomial for the left-handed torus knot (2, 2t + 1). We use this to define a family of q-series, the simplest case of which is the generating function for strongly unimodal sequences. Special cases of these q-series are quantum modular forms, and at roots of unity, these are dual to the generalized Kontsevich-Zagier series introduced by the first author. This duality generalizes a result of Bryson, Pitman, Ono, and Rhoades. We also compute Hecke-type expansions for our family of q-series.

    Original languageEnglish
    Article number2
    JournalResearch in Mathematical Sciences
    Issue number1
    Publication statusPublished - Dec 1 2015

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Mathematics (miscellaneous)
    • Computational Mathematics
    • Applied Mathematics


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