TY - JOUR
T1 - Difference equation of the colored Jones polynomial for torus knot
AU - Hikami, Kazuhiro
N1 - Funding Information:
The author would like to thank S. Garoufalidis, J. Kaneko, A. N. Kirillov, G. Masbaum, H. Murakami, T. Takata, Y. Yokota, D. Zagier and S. Zwegers for discussions. This work is supported in part by Grant-in-Aid for Young Scientists from the Ministry of Education, Culture, Sports, Science and Technology of Japan.
PY - 2004/11
Y1 - 2004/11
N2 - 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.
AB - 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.
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U2 - 10.1142/S0129167X04002582
DO - 10.1142/S0129167X04002582
M3 - Article
AN - SCOPUS:11244292505
SN - 0129-167X
VL - 15
SP - 959
EP - 965
JO - International Journal of Mathematics
JF - International Journal of Mathematics
IS - 9
ER -