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

This article is cited in 4 scientific papers (total in 4 papers)

Research Papers

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

K. Hikamia, A. N. Kirillovb

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

Abstract: Relationships between the quantum invariants of the torus knots $\tau_{3,2^k}$ andsome $q$-series identities are studied. In particular, new generalizations of the Slater identities (83) and (86) are obtained.

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English version:
St. Petersburg Mathematical Journal, 2006, 17:1, 143–156

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Received: 07.09.2004
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Citation: 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), 143–156

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://www.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}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Hikami K., “Quantum invariants, modular forms, and lattice points II”, J. Math. Phys., 47:10 (2006), 102301, 32 pp.  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Hikami K., “On the quantum invariants for the spherical Seifert manifolds”, Comm. Math. Phys., 268:2 (2006), 285–319  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. 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.  crossref  mathscinet  zmath  isi  scopus
    4. Hikami K., “Asymptotics of the colored Jones polynomial and the A-polynomial”, Nuclear Phys. B, 773:3 (2007), 184–202  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
  • Алгебра и анализ St. Petersburg Mathematical Journal
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