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

Research output: Contribution to journalArticle

14 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 languageEnglish
Pages (from-to)175-197
Number of pages23
JournalRamanujan Journal
Volume11
Issue number2
DOIs
Publication statusPublished - Apr 1 2006
Externally publishedYes

Fingerprint

Q-series
L-function
Generating Function
Quantum Invariants
Torus knot
Derivative
Roots of Unity
Integer
Generalization

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

Q-Series and L-functions related to half-derivatives of the Andrews-Gordon identity. / Hikami, Kazuhiro.

In: Ramanujan Journal, Vol. 11, No. 2, 01.04.2006, p. 175-197.

Research output: Contribution to journalArticle

@article{a9dc67aa865e480c88de923b761d9f63,
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",
year = "2006",
month = "4",
day = "1",
doi = "10.1007/s11139-006-6506-1",
language = "English",
volume = "11",
pages = "175--197",
journal = "Ramanujan Journal",
issn = "1382-4090",
publisher = "Springer Netherlands",
number = "2",

}

TY - JOUR

T1 - Q-Series and L-functions related to half-derivatives of the Andrews-Gordon identity

AU - Hikami, Kazuhiro

PY - 2006/4/1

Y1 - 2006/4/1

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.

UR - http://www.scopus.com/inward/record.url?scp=33744752446&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33744752446&partnerID=8YFLogxK

U2 - 10.1007/s11139-006-6506-1

DO - 10.1007/s11139-006-6506-1

M3 - Article

AN - SCOPUS:33744752446

VL - 11

SP - 175

EP - 197

JO - Ramanujan Journal

JF - Ramanujan Journal

SN - 1382-4090

IS - 2

ER -