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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 

 

Hypergeometric generating function of $ L$-function, Slater's identities, and quantum invariant


Authors: K. Hikami and A. N. Kirillov
Original publication: Algebra i Analiz, tom 17 (2005), nomer 1.
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
Published electronically: January 19, 2006
MathSciNet review: 2140679
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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.


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Additional 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

DOI: https://doi.org/10.1090/S1061-0022-06-00897-1
Keywords: Knot invariants, Virasoro minimal models, Slater's identities
Received by editor(s): September 7, 2004
Published electronically: January 19, 2006
Dedicated: Dedicated to Ludwig Dmitrievich Faddeev on the occasion of his seventieth birthday
Article copyright: © Copyright 2006 American Mathematical Society