A sharp Bombieri inequality, logarithmic energy and well conditioned\n polynomials

2019/12/11 by Ujué Etayo, Etayo, Ujué · 1 citation
Mathematics · #11C08 #11J99 #30C15 #30E10 #31C12 #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1912.05521

openalex publication_date 2019/12/11 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

In this paper we explore the connections between minimizers of the discrete\nlogarithmic energy on the 2-dimensional sphere, univariate polynomials with\noptimal condition number in the Shub-Smale sense and a quotient involving norms\nof polynomials. Our main results are that polynomials with optimal condition\nnumber produce spherical points with small logarithmic energy (the reverse\nresult was already known) and a sharp Bombieri type inequality for univariate\npolynomials with complex coefficients.\n

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