A sharp Bombieri inequality, logarithmic energy and well conditioned polynomials
Classical Analysis and ODEs
2019-12-12 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1912.05521,
title = {A sharp Bombieri inequality, logarithmic energy and well conditioned polynomials},
author = {Ujué Etayo},
journal= {arXiv preprint arXiv:1912.05521},
year = {2019}
}