On self-reciprocal polynomials at a point on the unit circle
Bull. Korean Math. Soc. 2009 Vol. 46, No. 6, 1153-1158
https://doi.org/10.4134/BKMS.2009.46.6.1153
Published online November 1, 2009
Seon-Hong Kim
Sookmyung Women's University
Abstract : Given two integral self-reciprocal polynomials having the same modulus at a point $z_0$ on the unit circle, we show that the minimal polynomial of $z_0$ 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 $z_0$ on the unit circle such that the two polynomials have the same modulus at $z_0$.
Keywords : self-reciprocal polynomials, zeros, unit circle
MSC numbers : Primary 30C15; Secondary 26C10
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