Geodesic
On the distribution of the roots of polynomial $z^k-z^{k-1}-\dots - z-1$
Commentationes Mathematicae Universitatis Carolinae, Tome 62 (2021) no. 3, pp. 291-296.

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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.
DOI : 10.14712/1213-7243.2021.025
Classification : 11B39, 12F10
Keywords: polynomial root distribution 
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Gómez, Carlos A.; Luca, Florian. On the distribution of the roots of polynomial $z^k-z^{k-1}-\dots - z-1$. Commentationes Mathematicae Universitatis Carolinae, Tome 62 (2021) no. 3, pp. 291-296. doi : 10.14712/1213-7243.2021.025. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2021.025/

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