On the Sendov conjecture for polynomials with simple zeros

Robert Dalmasso (1)

1 EDP - Equations aux Dérivées Partielles

The Sendov conjecture asserts that if all the zeros of a polynomial p lie in the closed unit disk then there must be a zero of p′ within unit distance of each zero. In this paper we give a partial result when p has simple zeros.

Mots clés: Sendov's conjecture; polynomial; simple zeros; Walsh's Coincidence Theorem

Domaines: Analyse classique [math.CA]; Equations aux dérivées partielles [math.AP]

Robert Dalmasso. On the Sendov conjecture for polynomials with simple zeros. 2018. ⟨hal-01790791⟩