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

Kazuhiro Hikami
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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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Kazuhiro Hikami. 2003-05-10. q-series and L-functions related to half-derivatives of the Andrews--Gordon identity. https://doi.org/10.1007/s11139-006-6506-1

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