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St. Petersburg Mathematical Journal
ISSN 1547-7371(e) ISSN 1061-0022(p)

     
     

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

Author(s): K. Hikami; A. N. Kirillov
Original publication: Algebra i Analiz, tom 17 (2005), vypusk 1.
Journal: St. Petersburg Math. J. 17 (2006), 143-156.
MSC (2000): Primary 11B65, 57M27, 05A30, 11F23
Posted: January 19, 2006
MathSciNet review: 2140679
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Abstract | References | Similar articles | Additional information

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: 10.1090/S1061-0022-06-00897-1
PII: S 1061-0022(06)00897-1
Keywords: Knot invariants, Virasoro minimal models, Slater's identities
Received by editor(s): 7/SEP/2004
Posted: January 19, 2006
Dedicated: Dedicated to Ludwig Dmitrievich Faddeev on the occasion of his seventieth birthday
Copyright of article: Copyright 2006, American Mathematical Society




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