关键词: Jones polynomial, zeros, torus knot, 2-bridge knot

Abstract: 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 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. 

Key words: Jones polynomial, zeros, torus knot, 2-bridge knot