Asymptotic Bohr Radius for the Polynomials in One Complex Variable

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 $R_n={1\over 3}+{π^2\over {3n^2}}+o({1\over n^2})$. We shall prove this conjecture is true in this paper.

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