q-Series and L-functions related to half-derivatives of the Andrews-Gordon identity |
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| Authors: | Kazuhiro Hikami |
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| Institution: | (1) Department of Physics, Graduate School of Science, University of Tokyo, Hongo 7-3-1, Bunkyo, Tokyo 113-0033, Japan |
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| Abstract: | Studied is a generalization of Zagier’s q-series identity. We introduce a generating function of L-functions at non-positive integers, which is regarded as a half-differential of the Andrews-Gordon q-series. When q is a root of unity, the generating function coincides with the quantum invariant for the torus knot.
2000 Mathematics Subject Classification Primary—11F67, 57M27, 05A30, 11F23 |
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| Keywords: | q-hypergeometric function Modular form Rogers-Ramanujan identity Andrews-Gordon identity L-function Quantum invariant Colored Jones polynomial Torus knot |
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