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

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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.

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Authors and Affiliations

  1. Department of Physics, Graduate School of Science, University of Tokyo, Hongo 7-3-1, Bunkyo, Tokyo, 113-0033, Japan

    Kazuhiro Hikami

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  1. Kazuhiro Hikami
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Correspondence to Kazuhiro Hikami.

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2000 Mathematics Subject Classification Primary—11F67, 57M27, 05A30, 11F23

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Hikami, K. q-Series and L-functions related to half-derivatives of the Andrews-Gordon identity. Ramanujan J 11, 175–197 (2006). https://doi.org/10.1007/s11139-006-6506-1

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  • DOI: https://doi.org/10.1007/s11139-006-6506-1

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