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

Authors
Kim, Seon-Hong
Issue Date
Nov-2009
Publisher
KOREAN MATHEMATICAL SOC
Keywords
self-reciprocal polynomials; zeros; unit circle
Citation
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, v.46, no.6, pp.1153 - 1158
Journal Title
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY
Volume
46
Number
6
Start Page
1153
End Page
1158
URI
https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/13659
DOI
10.4134/BKMS.2009.46.6.1153
ISSN
1015-8634
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).
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