Binary polynomial power sums vanishing at roots of unity

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 $n=1,2\dots$. We estimate the orders of these roots of unity in terms of the degrees and the heights of the polynomials $c_i$ and $f_i$.

To appear in Acta Arithmetica

References in corpus (1)

• An effective lower bound for the height of algebraic numbers