A SHARP BOMBIERI INEQUALITY, LOGARITHMIC ENERGY AND WELL CONDITIONED POLYNOMIALS

摘要

We explore the connections between minimizers of the discrete logarithmic energy on the sphere S-2, univariate polynomials with optimal condition number in the Shub-Smale sense and a quotient involving norms of polynomials. Our main results are that polynomials with optimal condition number produce spherical points with small logarithmic energy (the reverse result was already known) and a sharp Bombieri type inequality for univariate polynomials with complex coefficients.