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

  • Published : 2009.11.30

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

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. https://doi.org/10.4134/BKMS.2007.44.3.461