On the arguments of the roots of the generalized Fibonacci polynomial

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 Ψ k ( z ) = z k −z k− 1 −⋯−1, k ⩾ 1, are uniformly distributed around the unit circle in the strong quantitative form, confirming a co...

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Bibliographic Details
Published inLithuanian mathematical journal Vol. 63; no. 3; pp. 249 - 253
Main Authors Alahmadi, Adel, Klurman, Oleksiy, Luca, Florian, Shoaib, Hatoon
Format Journal Article
LanguageEnglish
Published New York Springer US 01.07.2023
Springer Nature B.V
Subjects
Actuarial Sciences
Mathematics
Mathematics and Statistics
Number Theory
Ordinary Differential Equations
Polynomials
Probability Theory and Stochastic Processes
secondary 11B39 12D10 30C15
primary 11C08
zeros of generalized Fibonacci polynomials
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Summary: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 Ψ k ( z ) = z k −z k− 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 z k − z k− 1 − ⋯ −z − 1, 62(3):291–296, 2021].
Bibliography:ObjectType-Article-1
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ISSN:0363-1672
1573-8825
DOI:10.1007/s10986-023-09604-0