The goal of this paper is to obtain some comparison inequalities for a linear operator between polynomials in the plane. The polynomials under study have constraints on their zeros and the estimates ...

Let N*(m) be the minimal length of a polynomial with ± 1 coefficients divisible by $(x - 1)^m$. Byrnes noted that $N^{*}(m) \leq 2^m$ for each m, and asked whether ...