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 language | English |
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Article number | rnm022 |
Journal | International Mathematics Research Notices |
Volume | 2007 |
DOIs | |
Publication status | Published - Dec 1 2007 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Mathematics(all)