Q-Series and L-functions related to half-derivatives of the Andrews-Gordon identity

Ramanujan Journal

Volumn 11, Issue 2, 2006, Pages 175-197

  Hikami, Kazuhiro ^a  

^a UNIVERSITY OF TOKYO   (Japan)

Author keywords

Andrews Gordon identity; Colored Jones polynomial; L function; Modular form; q hypergeometric function; Quantum invariant; Rogers Ramanujan identity; Torus knot

Indexed keywords

EID: 33744752446     PISSN: 13824090     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11139-006-6506-1     Document Type: Article

References (13)

1. Andrews, G.E.: The Theory of Partitions. Addison-Wesley, London (1976)
2. Andrews, G.E.: q-Series: Their development and application in analysis, number theory, combinatorics, physics, and computer algebra. AMS, Providence (1986)
3. Andrews, G.E.: Bailey's transform, lemma, chains and tree, in Special Functions 2000: Current Perspective and Future Directions, Bustoz, J., Ismail, M. E. H., and Suslov, S. K. (eds.), NATO Sci. Ser. II 30, Kluwer, Dordrecht, 1-22 (2001).
4. Andrews, G.E., Jiménez-Urroz, J. Ono, K.: q-series identities and values of certain L-functions. Duke Math. J. 108, 395-419 (2001)
5. Coogan, G.H., Ono, K.: A q-series identity and the arithmetic of Hurwitz zeta functions. Proc. Amer. Math. Soc. 131, 719-724 (2002).
6. Gasper, G., Rahman, M.: Basic Hypergeometric Series, Encyclopedia of Mathematics and Its Applications, Cambridge: Cambridge Univ. Press, (1990)
7. Hikami, K.: Volume conjecture and asymptotic expansion of q-series, preprint, to appear in Exp. Math. (2002)
8. Kashaev, R.M.: A link invariant from quantum dilogarithm. Mod. Phys. Lett. A 10, 1409-1418 (1995)
9. Lawrence, R., Zagier, D.: Modular forms and quantum invariants of 3-manifolds. Asian J. Math. 3, 93-107 (1999)
10. Lovejoy, J., Ono, K.: Hypergeometric generating functions for values of Dirichlet and other L-functions. Proc. Natl. Acad. Sci. 100, 6904-6909, (2003)
11. Murakami, H., Murakami, J.: The colored Jones polynomials and the simplicial volume of a knot, Acta Math. 186, 85-104 (2001)
12. Paule, P.: The concept of Bailey chain Séminaire Lotharingien de Combinatoire B18f (1987).
13. Zagier, D.: Vassiliev invariants and a strange identity related to the Dedekind eta-function. Topology 40, 945-960 (2001)