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Reciprocal polynomials with all zeros on the unit circle

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Abstract

Let f(x)=a d x d+a d−1 x d−1+⋅⋅⋅+a 0∈ℝ[x] be a reciprocal polynomial of degree d. We prove that if the coefficient vector (a d ,a d−1,…,a 0) or (a d−1,a d−2,…,a 1) is close enough, in the l 1-distance, to the constant vector (b,b,…,b)∈ℝd+1 or ℝd−1, then all of its zeros have moduli 1.

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  1. Department of Mathematics, Chonnam National University, Gwangju, 500-757, Republic of Korea

    Do Yong Kwon

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  1. Do Yong Kwon
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Correspondence to Do Yong Kwon.

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Kwon, D.Y. Reciprocal polynomials with all zeros on the unit circle. Acta Math Hung 131, 285–294 (2011). https://doi.org/10.1007/s10474-011-0090-6

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  • DOI: https://doi.org/10.1007/s10474-011-0090-6

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