Year: 2004
Type: article
Abstract: Define S ( n , β ) S(n,\beta ) to be the set of complex polynomials of degree n ≥ 2 n\ge 2 with all roots in the unit disk and at least one root at β \beta . For a polynomial P P , define | P | β |P|_\beta to be the distance between β \beta and the closest root of the derivative P ′ P’ . Finally, define r n ( β ) = sup { | P | β : P ∈ S ( n , β ) } r_n(\beta )=\sup \{ |P|_\beta : P \in S(n,\beta ) \} . In this notation, a conjecture of Bl. Sendov claims that r n ( β ) ≤ 1 r_n(\beta )\le 1 . In this paper we investigate Sendov’s conjecture near the unit circle, by computing constants C 1 C_1
Author: Michael Miller
Institution: Le Moyne College
Language: Latvian
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W1484095440