Asymptotic Bohr Radius for the Polynomials in One Complex Variable

Abstract

We consider the Bohr radius $R_n$ for the class of complex polynomials in one variable of degree at most $n$. It was conjectured by R. Fournier in 2008 that $R_n=\frac{1}{3}+\frac{\ddot{I}{€}^2}{3n^2}+o(\frac{1}{n^2})$. We shall prove this conjecture is true in this paper.