Zeros of the Jones Polynomial for Torus Knots and 2-bridge Knots  

作　　者：HAN You-fa ZHANG Rong-wei WANG Lin-lin MA Xiao-sha 

机构地区：[1]School of Mathematics, Liaoning Normal University, Dalian 116029, China

出　　处：《Chinese Quarterly Journal of Mathematics》2014年第4期612-619,共8页数学季刊（英文版）

基　　金：Supported by the National Science Foundation of China（11471151）; Supported by Program for Liaoning Excellent Talents in University（LR2011031） Acknowledgment The authors would like to thank the referees for kind suggestions and many useful comments

摘　　要：We study zeros of the Jones polynomial and their distributions for torus knots and 2-bridge knots. We prove that e(2m+1)πi/2and e(2m+1)πi/4(m is a positive integer)can not be the zeros of Jones polynomial for torus knots T p,q by the knowledge of the trigonometric function. We elicit the normal form of Jones polynomials of the 2-bridge knot C(-2, 2, ···,(-1)r2) by the recursive form and discuss the distribution of their zeros.We study zeros of the Jones polynomial and their distributions for torus knots and 2-bridge knots. We prove that e^（2m＋1）πi/2 and e^（2m＋1）πi/4（m is a positive integer） can not be the zeros of Jones polynomial for torus knots Tp,q by the knowledge of the trigonometric function. We elicit the normal form of Jones polynomials of the 2-bridge knot C（-2, 2,…, （-1）^r2） by the recursive form and discuss the distribution of their zeros.

关 键 词：Jones polynomial ZEROS torus knot 2-bridge knot 

分 类 号：O189.3[理学—数学]