Abstract.The maximum modulus on \z\ = r < I of a polynomial of degree n not vanishing in \z\ < 1 is estimated in terms of its maximum modulus on \z\ = 1 and certain of its coefficients. Some other related problems are also considered.

Abstract. In this paper we study the growth of polynomials of degree n having no zeros in |z| < κ , where κ is an arbitrary positive number. Using the notation M(p; t) = max |z|=t |p(z)| we measure the growth of p by estimating M(p; t)/M(p; 1) from above for any t > 1 , and from below for any t < 1 . (2000): 30A10, 30C10, 30E10; 30C15. Mathematics subject classification

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