纽结多项式零点的性质  

Properties of zeros of the knot polynomial

作　　者：韩友发[1] 赵晓然 孙艺丹 王英姣 HAN Youfa;ZHAO Xiaoran;SUN Yidan;WANG Yingjiao(School of Mathematics,Liaoning Normal University,Dalian 116029,Chian)

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《辽宁师范大学学报（自然科学版）》2018年第3期315-320,共6页Journal of Liaoning Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11471151)

摘　　要：研究了链环和纽结的Jones多项式性质以及零点分布性质.利用的Jones多项式的某些点取值的性质、微分性质以及三角函数的性质,特别是正弦函数和余弦函数的性质,研究了环面纽结多项式的性质和它们多项式根的性质,同时讨论了单位根的有关性质,讨论了它们之间的内在联系,从而给出某些单位根不是环面纽结多项式的根,证明了当6≤n≤8时,单位根e2p+1/nπi不是环面结Tp,q(其中,(p,q)=1)的琼斯多项式的零点.这些性质的研究将有利于研究整系数多项式与纽结多项式之间的关系.This paper studies the links and knots of the Jones polynomial and their zero points distributions by using some properties of the Jones polynomial for knots and the related knowledge of trigonometric function,particularly,properties of sine function and cosine function.It studies properties of torus knot polynomial and their zeros.Meantime,the properties of unit root are discussed.It concludes that some unit roots are not zeros of knot polynomial,that is,e2p＋1/nπi（6≤n≤8）,are not the zeros of the Jones polynomial for torus knots Tp,q（while（p,q）=1）.It is good to study the relationship between integral coefficient polynomials and knot polynomials.

关 键 词：JONES多项式 环面结 零点 

分 类 号：O189.3[理学—数学]