Binary polynomial power sums vanishing at roots of unity

Bilu, Yuri; Luca, Florian

doi:10.4064/aa200511-12-9

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Binary polynomial power sums vanishing at roots of unity

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Luca, Florian
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.4064/aa200511-12-9
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Citation

Bilu, Y., & Luca, F. (2021). Binary polynomial power sums vanishing at roots of unity. Acta Arithmetica, 198(2), 195-217. doi:10.4064/aa200511-12-9.

Cite as: https://hdl.handle.net/21.11116/0000-0008-AE00-4

Abstract

Let $c_1(x),c_2(x),f_1(x),f_2(x)$ be polynomials with rational coefficients.
With obvious exceptions, there can be at most finitely many roots of unity among the zeros of the polynomials $c_1(x)f_1(x)^n+c_2(x)f_2(x)^n$ with
$n=1,2\ldots$. We estimate the orders of these roots of unity in terms of the degrees and the heights of the polynomials $c_i$ and $f_i$.