Asymptotics of the Bohr radius for polynomials of fixed degree

We obtain a characterization and precise asymptotics of the Bohr radius for the class of complex polynomials in one variable. Our work is based on the notion of bound-preserving operators. Key words: Bohr radius, complex polynomials, bound preserving operators. PACS: 41A25 1 Introduction and statement of the result Let D denote the unit disc {z | |z | < 1} of the complex plane C and H(D) the vector space of functions analytic in D endowed with the norm |f |D = su