EXACT INEQUALITIES FOR THE NORMS OF FACTORS OF POLYNOMIALS

This paper addresses a number of questions concerning the size of fact ors of polynomials. Let p be a monic algebraic polynomial of degree n and suppose q1q2...q(i) is a monic factor of p of degree m. Then we ca n, in many cases, exactly determine [GRAPHICS] Here parallel-to . para llel-to is the supremum norm either on [-1, 1] or on {\z\ less-than-or -equal-to 1}. We do this by showing that, in the interval case, for ea ch m and n, the n-th Chebyshev polynomial is extremal. This extends wo rk of Gel'fond, Mahler, Granville, Boyd and others. A number of varian ts of this problem are also considered.