Difference equation of the colored Jones polynomial for torus knot

Research output: Contribution to journalArticle

29 Citations (Scopus)

Abstract

We prove that the N-colored Jones polynomial for the torus knot T s,t satisfies the second order difference equation, which reduces to the first order difference equation for a case of T2,2m+1. We show that the A-polynomial of the torus knot can be derived from the difference equation. Also constructed is a q-hypergeometric type expression of the colored Jones polynomial for T2,2m+1.

Original languageEnglish
Pages (from-to)959-965
Number of pages7
JournalInternational Journal of Mathematics
Volume15
Issue number9
DOIs
Publication statusPublished - Nov 1 2004
Externally publishedYes

Fingerprint

Colored Jones Polynomial
Torus knot
Difference equation
Second-order Difference Equations
A-polynomial
First-order

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Difference equation of the colored Jones polynomial for torus knot. / Hikami, Kazuhiro.

In: International Journal of Mathematics, Vol. 15, No. 9, 01.11.2004, p. 959-965.

Research output: Contribution to journalArticle

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