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 ...

We study an infinite family of lower and upper bounds on the modulus of zeros of complex polynomials derived by Kalantari. We first give a simple characterization of these bounds which leads to an ...