ON SELF-RECIPROCAL POLYNOMIALS AT A POINT ON THE UNIT CIRCLE

Title & Authors
ON SELF-RECIPROCAL POLYNOMIALS AT A POINT ON THE UNIT CIRCLE
Kim, Seon-Hong;

Abstract
Given two integral self-reciprocal polynomials having the same modulus at a point $\small{z_0}$ on the unit circle, we show that the minimal polynomial of $\small{z_0}$ is also self-reciprocal and it divides an explicit integral self-reciprocal polynomial. Moreover, for any two integral self-reciprocal polynomials, we give a sufficient condition for the existence of a point $\small{z_0}$ on the unit circle such that the two polynomials have the same modulus at $\small{z_0}$.
Keywords
self-reciprocal polynomials;zeros;unit circle;
Language
English
Cited by
References
1.
R. A. DeVore and G. G. Lorentz, Constructive Approximation, Springer-Verlag, Berlin, 1993

2.
S.-H. Kim, The zeros of certain family of self-reciprocal polynomials, Bull. Korean Math. Soc. 44 (2007), no. 3, 461–473.