  In this paper we explore the connections between minimizers of the discrete
logarithmic energy on the 2-dimensional sphere, 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.
