Hecke-type formulas for families of unified Witten-Reshetikhin-Turaev invariants

Kazuhiro Hikami, Jeremy Lovejoy

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


Every closed orientable 3-manifold can be constructed by surgery on a link in S3. In the case of surgery along a torus knot, one obtains a Seifert fibered manifold. In this paper we consider three families of such manifolds and study their unified Witten- Reshetikhin-Turaev (WRT) invariants. Thanks to recent computation of the coefficients in the cyclotomic expansion of the colored Jones polynomial for (2, 2t + 1)-torus knots, these WRT invariants can be neatly expressed as q-hypergeometric series which converge inside the unit disk. Using the Rosso-Jones formula and some rather non-standard techniques for Bailey pairs, we find Hecke-type formulas for these invariants. We also comment on their mock and quantum modularity.

Original languageEnglish
Pages (from-to)249-272
Number of pages24
JournalCommunications in Number Theory and Physics
Issue number2
Publication statusPublished - 2017

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Mathematical Physics
  • Physics and Astronomy(all)


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