2011/06/21 by Jérôme Dégot, Dégot, Jérôme
Mathematics · #30C10 #30C15 (Primary) 12D10 (Secondary) #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #FOS: Mathematics #Mathematical functions and polynomials #Meromorphic and Entire Functions #math.CV #msc:12D10 #msc:30C10 #msc:30C15
paper · pdf · doi:10.48550/arxiv.1106.4126
14 pages, 5 figures
openalex publication_date 2011/06/21 · arxiv created 2011/11/15 · arxiv updated 2011/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Sendov conjecture tells that if P denotes a complex polynomial having all his zeros in the closed unit disk and a denote a zero of P, the closed disk of center a and radius 1 contains a zero of the derivative P'. The main result of this paper is a proof of Sendov conjecture when the polynomial P has a degree higher than a fixed integer N. We will give estimates of its integer N in terms of |a|. To obtain this result, we will study the geometry of the zeros and critical points (i.e. zeros of P') of a polynomial which would contradict Sendov conjecture.