Minimizing norms of polynomials under constraints on the distribution of the roots (Q1909538)

In this paper we study the links between the distribution of the roots of a complex polynomial and the ratio between various norms and the extremal two coefficients of the polynomial. Precisely, for polynomials with all roots in a convex sector of the complex plane, we study the distribution of the roots which minimizes the ratio related either to the supremum norm on the unit disc or the Euclidean norm, or Bombieri's norm, a weighted Euclidean norm.