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

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

2003-03-20

arxiv.org/abs/math/0303250v2

Ramanujan J. 11, 175-197 (2006)

Mathematics

Number Theory

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

Scientific paper

10.1007/s11139-006-6506-1

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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