Hypergeometric generating function of $L$-function, Slater’s identities, and quantum invariant
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- by K. Hikami and A. N. Kirillov
- St. Petersburg Math. J. 17 (2006), 143-156
- DOI: https://doi.org/10.1090/S1061-0022-06-00897-1
- Published electronically: January 19, 2006
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Abstract:
Relationships between the quantum invariants of the torus knots $\mathcal {T}_{3,2^k}$ and some $q$-series identities are studied. In particular, new generalizations of the Slater identities (83) and (86) are obtained.References
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Bibliographic Information
- K. Hikami
- Affiliation: Department of Physics, Graduate School of Science, University of Tokyo, Hongo 7–3–1, Bunkyo, Tokyo 113–0033, Japan
- Email: hikami@phys.s.u-tokyo.ac.jp
- A. N. Kirillov
- Affiliation: Research Institute of Mathematical Sciences (RIMS), Kyoto University, Kyoto 606-8502, Japan
- Email: kirillov@kurims.kyoto-u.ac.jp
- Received by editor(s): September 7, 2004
- Published electronically: January 19, 2006
- © Copyright 2006 American Mathematical Society
- Journal: St. Petersburg Math. J. 17 (2006), 143-156
- MSC (2000): Primary 11B65, 57M27, 05A30, 11F23
- DOI: https://doi.org/10.1090/S1061-0022-06-00897-1
- MathSciNet review: 2140679
Dedicated: Dedicated to Ludwig Dmitrievich Faddeev on the occasion of his seventieth birthday