Some remarks on rotation theorems for complex polynomials

TL;DR

This paper investigates how the argument of complex polynomials with zeros inside the unit disk changes as the point moves along the boundary, providing estimates for the rate of change.

Contribution

It offers new estimates for the argument variation of polynomials with zeros in the unit disk, enhancing understanding of their boundary behavior.

Findings

Derived bounds on argument change for such polynomials

Improved understanding of boundary argument variation

Potential applications in complex analysis and polynomial stability

Abstract

For any complex polynomial P having all its zeros in the unit disk, we estimate the rate of change of the argument P (z) when the point z runs through the boundary of this disk.