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Journal Article

#### Binary polynomial power sums vanishing at roots of unity

##### External Resource

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

(Publisher version)

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##### Fulltext (public)

2005.05500.pdf

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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 $f_i$.

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 $f_i$.