On self-reciprocal polynomials at a point on the unit circle
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Given two integral self-reciprocal polynomials having the sa\-me 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.
Abstract
Given two integral self-reciprocal polynomials having the sa\-me 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.
참고문헌 (2)
- R. A. DeVore, "Constructive Approximation" (1993), Springer-Verlag
- 김선홍, "The zeros of certain family of self-reciprocal polynomials", 대한수학회보, 44(3), pp.461~473 (2007), 대한수학회