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

Kazuhiro Hikami

doi:10.1007/s11139-006-6506-1

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

Kazuhiro Hikami

Research output: Contribution to journal › Article › peer-review

24 Citations (Scopus)

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.

Original language	English
Pages (from-to)	175-197
Number of pages	23
Journal	Ramanujan Journal
Volume	11
Issue number	2
DOIs	https://doi.org/10.1007/s11139-006-6506-1
Publication status	Published - Apr 2006
Externally published	Yes

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1007/s11139-006-6506-1

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title = "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.",

author = "Kazuhiro Hikami",

note = "Funding Information: Acknowledgments The author would like to thank Hitoshi Murakami for bringing [13] to our attention. He thanks Ken Ono for useful communications. Thanks are also due to George Andrews for sending [3]. He thanks Don Zagier for suggesting a proof of Theorem 17. This work is supported in part by the Sumitomo foundation.",

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doi = "10.1007/s11139-006-6506-1",

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AU - Hikami, Kazuhiro

N1 - Funding Information: Acknowledgments The author would like to thank Hitoshi Murakami for bringing [13] to our attention. He thanks Ken Ono for useful communications. Thanks are also due to George Andrews for sending [3]. He thanks Don Zagier for suggesting a proof of Theorem 17. This work is supported in part by the Sumitomo foundation.

PY - 2006/4

Y1 - 2006/4

N2 - 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.

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

Abstract

All Science Journal Classification (ASJC) codes

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