Hecke type formula for unifiedwitten-reshetikhin-turaev invariants as higher-order mock theta functions

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

We study the unified Witten-Reshetikhin-Turaev invariant for the Brieskorn homology sphere S(2, 3, 6 p-1) based on the cyclotomic expansion of the colored Jones polynomial for twist knot Kp. We discuss that the invariant has the same asymptotic expansion in N → 8 with the Ramanujan mock theta function when q is the root of unity q = exp(2 π i/N), and that it can be regarded as the (6 p - 1)-th order mock theta function. It is shown that it has the Hecke-type formula as in the case of the mock theta functions, though the quadratic form is positive definite while indefinite for almost all the Ramanujan mock theta functions.

Original languageEnglish
Article numberrnm022
JournalInternational Mathematics Research Notices
Volume2007
DOIs
Publication statusPublished - Dec 1 2007
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Fingerprint Dive into the research topics of 'Hecke type formula for unifiedwitten-reshetikhin-turaev invariants as higher-order mock theta functions'. Together they form a unique fingerprint.

  • Cite this