On the arguments of the roots of the generalized Fibonacci polynomial

Abstract

We revisit the classical subject of equidistribution of the roots of Littlewood-type polynomials. More precisely, we show that the roots of the family of polynomials Ψk(z) = zk−zk−1−⋯−1, k ⩾ 1, are uniformly distributed around the unit circle in the strong quantitative form, confirming a conjecture from [C.-A. Gómez and F. Luca, Commentat. Math. Univ. Carol., On the distribution of roots of zk − zk−1−⋯−z − 1, 62(3):291–296, 2021].