메뉴 건너뛰기




Volumn 12, Issue 3, 2003, Pages 319-337

Volume conjecture and asymptotic expansion of q-series

Author keywords

Hyperbolic volume; Jones polynomial; Rogers Ramanujan identity

Indexed keywords


EID: 1642365774     PISSN: 10586458     EISSN: 1944950X     Source Type: Journal    
DOI: 10.1080/10586458.2003.10504502     Document Type: Article
Times cited : (23)

References (26)
  • 1
    • 0000513672 scopus 로고    scopus 로고
    • (/-Series Identities and Values of Certain L- Functions
    • G. E. Andrews, J. Jiménez-Urroz, and K. Ono. “(/-Series Identities and Values of Certain L- Functions.” Duke Math. J. 108 (2001), 395-419.
    • (2001) Duke Math. J. , vol.108 , pp. 395-419
    • Andrews, G.E.1    Jiménez-Urroz, J.2    Ono, K.3
  • 5
    • 0035974536 scopus 로고    scopus 로고
    • Hyperbolic Structure Arising from a Knot Invariant
    • K. Hikami. “Hyperbolic Structure Arising from a Knot Invariant.” Int. J. Mod. Phys. A 16 (2001), 3309-3333.
    • (2001) Int. J. Mod. Phys. A , vol.16 , pp. 3309-3333
    • Hikami, K.1
  • 7
    • 0001281096 scopus 로고
    • A Link Invariant from Quantum Dilogarithm
    • R. M. Kashaev. “A Link Invariant from Quantum Dilogarithm.” Mod. Phys. Lett. A 10 (1995), 1409-1418.
    • (1995) Mod. Phys. Lett. A , vol.10 , pp. 1409-1418
    • Kashaev, R.M.1
  • 8
    • 0000356516 scopus 로고    scopus 로고
    • The Hyperbolic Volume of Knots from Quantum Dilogarithm
    • R. M. Kashaev. “The Hyperbolic Volume of Knots from Quantum Dilogarithm.” Lett. Math. Phys. 39 (1997), 269-275.
    • (1997) Lett. Math. Phys. , vol.39 , pp. 269-275
    • Kashaev, R.M.1
  • 9
    • 0012381015 scopus 로고    scopus 로고
    • Proof of the Volume Conjecture for Torus Knots
    • R. M. Kashaev and O. Tirkko- nen. “Proof of the Volume Conjecture for Torus Knots.” Zap. Nauch. Sem. POMI 269 (2000), 262-268.
    • (2000) Zap. Nauch. Sem. POMI , vol.269 , pp. 262-268
    • Kashaev, R.M.1    Tirkkonen, O.2
  • 10
    • 21144466962 scopus 로고
    • Chern- Simons Invariants of 3-Manifolds Decomposed along Tori and the Circle Bundle over the Representation Space of T2
    • P. Kirk and E. Klassen. “Chern- Simons Invariants of 3-Manifolds Decomposed along Tori and the Circle Bundle over the Representation Space of T2.” Commun. Math. Phys. 153 (1993), 521-557.
    • (1993) Commun. Math. Phys. , vol.153 , pp. 521-557
    • Kirk, P.1    Klassen, E.2
  • 11
    • 84966232256 scopus 로고
    • Representations of Knot Groups in SU(2)
    • E. P. Klassen. “Representations of Knot Groups in SU(2).” Trans. Amer. Math. Soc. 326 (1991), 795-828.
    • (1991) Trans. Amer. Math. Soc. , vol.326 , pp. 795-828
    • Klassen, E.P.1
  • 12
    • 84973933723 scopus 로고
    • The Coloured Jones Function and Alexander Polynomial for Torus Knots
    • H. R. Morton. “The Coloured Jones Function and Alexander Polynomial for Torus Knots.” Proc. Cambridge Philos. Soc. 117 (1995), 129-135.
    • (1995) Proc. Cambridge Philos. Soc. , vol.117 , pp. 129-135
    • Morton, H.R.1
  • 13
    • 1642396411 scopus 로고    scopus 로고
    • The Asymptotic Behavior of the Colored Jones Function of a Knot and Its Volume
    • edited by T. Kohno, Tokyo: Univ. Tokyo
    • H. Murakami. “The Asymptotic Behavior of the Colored Jones Function of a Knot and Its Volume.” In Art of Low Dimensional Topology VI, edited by T. Kohno, pp. 87-96. Tokyo: Univ. Tokyo, 2000.
    • (2000) Art of Low Dimensional Topology VI , pp. 87-96
    • Murakami, H.1
  • 14
    • 0002742222 scopus 로고    scopus 로고
    • The Colored Jones Polynomials and the Simpli- cial Volume of a Knot
    • H. Murakami and J. Murakami. “The Colored Jones Polynomials and the Simpli- cial Volume of a Knot.” Acta Math. 186 (2001), 85-104.
    • (2001) Acta Math , vol.186 , pp. 85-104
    • Murakami, H.1    Murakami, J.2
  • 15
    • 0036943077 scopus 로고    scopus 로고
    • Kashaevs Conjecture and the Chern-Simons Invariants of Knots and Links
    • H. Murakami, J. Murakami, M. Oka- moto, T. Takata, and Y. Yokota. “Kashaev’s Conjecture and the Chern-Simons Invariants of Knots and Links.” Exp. Math. 11 (2002), 427-435.
    • (2002) Exp. Math. , vol.11 , pp. 427-435
    • Murakami, H.1    Murakami, J.2    Okamoto, M.3    Takata, T.4    Yokota, Y.5
  • 16
    • 0000459324 scopus 로고
    • Volumes of Hyperbolic Three-Manifolds
    • W. Z. Neumann and D. Zagier. “Volumes of Hyperbolic Three-Manifolds.” Topology 24 (1985), 307-332.
    • (1985) Topology , vol.24 , pp. 307-332
    • Neumann, W.Z.1    Zagier, D.2
  • 17
    • 85023941456 scopus 로고    scopus 로고
    • PARI/GP, Version 2.0.14, Bordeaux. Available from World Wide Web
    • The PARI Group. PARI/GP, Version 2.0.14, Bordeaux. Available from World Wide Web (http://www.parigp-home.de/), 2000.
    • (2000)
  • 18
    • 84974403730 scopus 로고
    • Some Formulas Related to Dilogarithms, the Zeta Function and the Andrews-Gordon Identities
    • B. Richmond and G. Szekeres. “Some Formulas Related to Dilogarithms, the Zeta Function and the Andrews-Gordon Identities.” J. Austral. Math. Soc. (Series A) 31 (1981), 362-373.
    • (1981) J. Austral. Math. Soc. (Series A) , vol.31 , pp. 362-373
    • Richmond, B.1    Szekeres, G.2
  • 19
    • 0002743202 scopus 로고
    • On the Invariants of Torus Knots Derived from Quantum Groups
    • M. Rosso and V. Jones. “On the Invariants of Torus Knots Derived from Quantum Groups.” J. Knot Theory Ramifications 2 (1993), 97-112.
    • (1993) J. Knot Theory Ramifications , vol.2 , pp. 97-112
    • Rosso, M.1    Jones, V.2
  • 21
    • 0032371155 scopus 로고    scopus 로고
    • Enumeration of Chord Diagrams and an Upper Bound for Vassiliev Invariants
    • A. Stoimenow. “Enumeration of Chord Diagrams and an Upper Bound for Vassiliev Invariants.” J. Knot Theory Its Ram. 7 (1998), 93-114.
    • (1998) J. Knot Theory Its Ram. , vol.7 , pp. 93-114
    • Stoimenow, A.1
  • 22
    • 85023915857 scopus 로고    scopus 로고
    • Hyperbolic Volume and the Jones Polynomial, Lecture notes of Ecole d’ete de Mathematiques ‘Invariants de nceuds et de varietes de dimension 3’
    • D. Thurston. Hyperbolic Volume and the Jones Polynomial, Lecture notes of Ecole d’ete de Mathematiques ‘Invariants de nceuds et de varietes de dimension 3’, Institut Fourier, 1999.
    • (1999) Institut Fourier
    • Thurston, D.1
  • 23
    • 0000093817 scopus 로고
    • The Yang-Baxter Equation and Invariants of Links
    • V. Turaev. “The Yang-Baxter Equation and Invariants of Links.” Invent. Math. 92 (1988), 527-553.
    • (1988) Invent. Math , vol.92 , pp. 527-553
    • Turaev, V.1
  • 25
    • 0001271705 scopus 로고
    • The η-Invariant of Hyperbolic 3- Manifolds
    • T. Yoshida. “The η-Invariant of Hyperbolic 3- Manifolds.” Invent. Math. 81 (1985), 473-514.
    • (1985) Invent. Math. , vol.81 , pp. 473-514
    • Yoshida, T.1
  • 26
    • 0001195414 scopus 로고    scopus 로고
    • Vassiliev Invariants and a Strange Identity Related to the Dedekind Eta-Function
    • D. Zagier. “Vassiliev Invariants and a Strange Identity Related to the Dedekind Eta-Function.” Topology 40 (2001), 945-960.
    • (2001) Topology , vol.40 , pp. 945-960
    • Zagier, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.