On the Zeros of Self-Reciprocal Polynomials Satisfying Certain Coefficient Conditions

Kim, Seon-Hong; Lee, Jung‐Hee

doi:10.4134/bkms.2010.47.6.1189

Cited by 1 publication

(2 citation statements)

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“…Other interesting results are the following: Konvalina & Matache [21] found conditions under which a PSR polynomial has at least one non-real zero on S. Kim & Park [22] and then Kim and Lee [23] presented conditions for which all the zeros of certain PSR polynomials lie on S (some open cases were also addressed by Botta & al. in [24]). Suzuki [25] presented necessary and sufficient conditions, relying on matrix algebra and differential equations, for all the zeros of PSR polynomials to lie on S. In [26] Botta & al.…”

Section: Real Self-reciprocal Polynomialsmentioning

confidence: 99%

Section: Real Self-reciprocal Polynomialsmentioning

confidence: 99%

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Polynomials with Symmetric Zeros

Vieira

2019

Polynomials - Theory and Application

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Polynomials whose zeros are symmetric either to the real line or to the unit circle are very important in mathematics and physics. We can classify them into three main classes: the self-conjugate polynomials, whose zeros are symmetric to the real line; the self-inversive polynomials, whose zeros are symmetric to the unit circle; and the self-reciprocal polynomials, whose zeros are symmetric by an inversion with respect to the unit circle followed by a reflection in the real line. Real selfreciprocal polynomials are simultaneously self-conjugate and self-inversive so that their zeros are symmetric to both the real line and the unit circle. In this survey, we present a short review of these polynomials, focusing on the distribution of their zeros.

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