Michael J. Miller

collaborators

2 papers

math.CV2003

The best possible quadratic refinement of Sendov's conjecture

Michael Miller

A conjecture of Sendov states that if a polynomial has all its roots in the unit disk and if $β$ is one of those roots, then within one unit of $β$ lies a root of the polynomial's…

math.CV2003

A quadratic approximation to the Sendov radius near the unit circle

Michael Miller

Define $S (n, β)$ to be the set of complex polynomials of degree $n \geq 2$ with all roots in the unit disk and at least one root at $β$ . For a polynomial $P$ , define $∣ P ∣_{β}$ to be th…