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

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.

21 pages, related papers can be found from http://gogh.phys.s.u-tokyo.ac.jp/~hikami/

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