Remarks on the Obrechkoff inequality

TL;DR

This paper improves and generalizes Obrechkoff's inequality concerning the distribution of zeros of polynomials with non-negative coefficients within a given angle, and examines the conditions for equality.

Contribution

The authors extend Obrechkoff's inequality and analyze the equality case, providing a broader understanding of zero distribution for such polynomials.

Findings

Enhanced bounds on the number of zeros within an angle

Generalized inequality applicable to a wider class of polynomials

Characterization of cases where equality holds

Abstract

Oberchkoff's inequality says that a polynomial of degree d with non-negative coefficients has at most 2ad/pi zeros in the angle {|arg z|<a}. We improve and generalize this inequality, and study the case of equality.