Carlos A. Gómez, Florian Luca
On the distribution of the roots of polynomial z^k-z^{k-1}-\dots - z-1

Abstract: We consider the polynomial f_k(z) = z^k-z^{k-1}-\cdots -z-1 for k\ge 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.

Keywords: polynomial root distribution

DOI: DOI 10.14712/1213-7243.2021.025
AMS Subject Classification: 12F10 11B39