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On the distribution of the roots of polynomial z(k) - z(k-1) - ... - z - 1
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On the distribution of the roots of polynomial z(k) - z(k-1) - ... - z - 1

Carlos A. Gomez and Florian Luca
Commentationes mathematicae Universitatis Carolinae, Vol.62(3), pp.291-296
01/01/2021
DOI: https://doi.org/10.14712/1213-7243.2021.025

Abstract

Mathematics Physical Sciences Science & Technology
We consider the polynomial f(k)(z) = z(k) - z(k-1) - ... - z - 1 for k >= 2 which arises as the characteristic polynomial of the k-generalized Fibonacci sequence. In this short paper, we give estimates for the absolute values of the roots of f(k)(z) which lie inside the unit disk.

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