On the distribution of the roots of polynomial $z^k-z^{k-1}-\cdots -z-1$

Gómez, Carlos A., and Luca, Florian. "On the distribution of the roots of polynomial $z^k-z^{k-1}-\dots - z-1$." Commentationes Mathematicae Universitatis Carolinae 62.3 (2021): 291-296. <http://eudml.org/doc/297693>.

@article{Gómez2021,
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.},
author = {Gómez, Carlos A., Luca, Florian},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {polynomial root distribution},
language = {eng},
number = {3},
pages = {291-296},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the distribution of the roots of polynomial $z^k-z^\{k-1\}-\dots - z-1$},
url = {http://eudml.org/doc/297693},
volume = {62},
year = {2021},
}

TY - JOUR
AU - Gómez, Carlos A.
AU - Luca, Florian
TI - On the distribution of the roots of polynomial $z^k-z^{k-1}-\dots - z-1$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2021
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 62
IS - 3
SP - 291
EP - 296
AB - 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.
LA - eng
KW - polynomial root distribution
UR - http://eudml.org/doc/297693
ER -