K. Hikami, A. N. Kirillov, “Hypergeometric generating function of $L$-function, Slater's identities, and quantum invariant”, Algebra i Analiz, 17:1 (2005), 190–208; St. Petersburg Math. J., 17:1 (2006), 143

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Algebra i Analiz, 2005, Volume 17, Issue 1, Pages 190–208 (Mi aa651)

This article is cited in 7 scientific papers (total in 7 papers)

Research Papers

Hypergeometric generating function of

L

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

K. Hikami^a, A. N. Kirillov^b

^a Department of Physics, Graduate School of Science, University of Tokyo, Japan
^b Research Institute of Mathematical Sciences, Kyoto University, Japan

Full-text PDF (653 kB) Citations (7)

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Abstract: Relationships between the quantum invariants of the torus knots

τ_{3, 2^{k}}

$\tau_{3,2^k}$ andsome

q

$q$ -series identities are studied. In particular, new generalizations of the Slater identities (83) and (86) are obtained.

Received: 07.09.2004

English version:
St. Petersburg Mathematical Journal, 2006, Volume 17, Issue 1, Pages 143–156
DOI: https://doi.org/10.1090/S1061-0022-06-00897-1

Bibliographic databases:

Document Type: Article

Language: English

Citation: K. Hikami, A. N. Kirillov, “Hypergeometric generating function of

L

$L$ -function, Slater's identities, and quantum invariant”, Algebra i Analiz, 17:1 (2005), 190–208; St. Petersburg Math. J., 17:1 (2006), 143–156

Citation in format AMSBIB

\Bibitem{HikKir05}

\by K.~Hikami, A.~N.~Kirillov

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

\jour Algebra i Analiz

\yr 2005

\vol 17

\issue 1

\pages 190--208

\mathnet{http://mi.mathnet.ru/aa651}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2140679}

\zmath{https://zbmath.org/?q=an:1136.11308}

\transl

\jour St. Petersburg Math. J.

\yr 2006

\vol 17

\issue 1

\pages 143--156

\crossref{https://doi.org/10.1090/S1061-0022-06-00897-1}

Linking options:

https://www.mathnet.ru/eng/aa651

https://www.mathnet.ru/eng/aa/v17/i1/p190

This publication is cited in the following 7 articles:

Yuya Murakami, “Witten–Reshetikhin–Turaev invariants and indefinite false theta functions for plumbing indefinite H-graphs”, J. Knot Theory Ramifications, 33:12 (2024)
Bijaoui C., Boden H.U., Myers B., Osburn R., Rushworth W., Tronsgard A., Zhou Sh., “Generalized Fishburn Numbers and Torus Knots”, J. Comb. Theory Ser. A, 178 (2021), 105355
Goswami A., Osburn R., “Quantum Modularity of Partial Theta Series With Periodic Coefficients”, Forum Math., 33:2 (2021), 451–463
Hikami K., “Hecke Type Formula for Unified Witten-Reshetikhin-Turaev Invariants as Higher-Order Mock Theta Functions”, Int. Math. Res. Not. IMRN, 2007, rnm022, 32 pp.
Hikami K., “Asymptotics of the colored Jones polynomial and the A-polynomial”, Nuclear Phys. B, 773:3 (2007), 184–202
Hikami K., “Quantum invariants, modular forms, and lattice points II”, J. Math. Phys., 47:10 (2006), 102301, 32 pp.
Hikami K., “On the quantum invariants for the spherical Seifert manifolds”, Comm. Math. Phys., 268:2 (2006), 285–319

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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References:	72
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