A STABILITY VERSION OF THE GAUSS–LUCAS THEOREM AND APPLICATIONS

DOI10.1017/S1446788719000284zbMath1446.26012arXiv1805.10454OpenAlexW2971982011WikidataQ127320686 ScholiaQ127320686MaRDI QIDQ5118912

Stefan Steinerberger

Publication date: 27 August 2020

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.10454

zbMATH Keywords

rootspolynomial dynamicszeroscritical pointsderivativesGauss-Lucas theorem

Mathematics Subject Classification ID

Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Real polynomials: location of zeros (26C10)

Related Items (9)

Distances between zeroes and critical points for random polynomials with i.i.d. zeroes ⋮ The flow of polynomial roots under differentiation ⋮ Unnamed Item ⋮ Dynamics of Zeroes Under Repeated Differentiation ⋮ On the local pairing behavior of critical points and roots of random polynomials ⋮ Leaky roots and stable Gauss-Lucas theorems ⋮ A nonlocal transport equation describing roots of polynomials under differentiation ⋮ On the zeros of the derivatives of certain polynomials ⋮ A nonlocal transport equation modeling complex roots of polynomials under differentiation

Cites Work

• Eine Bemerkung zum Satz von Gauß-Lucas
• Differentiators and the geometry of polynomials.
• Majorization of the critical points of a polynomial by its zeros
• Pairing of zeros and critical points for random polynomials
• The Gauss–Lucas theorem in an asymptotic sense
• The Distribution of Zeros of the Derivative of a Random Polynomial
• An Elementary Proof of Marden's Theorem
• On the zeros of a polynomial and its derivatives
• A refinement of the Gauss-Lucas theorem
• On the Zeros of a Polynomial and of Its Derivative
• Pairing between zeros and critical points of random polynomials with independent roots
• A contraction of the Lucas polygon
• Inverse spectral problem for normal matrices and the Gauss-Lucas theorem
• Critical points of random polynomials with independent identically distributed roots
• A note on the zeros of the sections of a partial fraction
• On the zeros of a polynomial and its derivative
• On the zeros of a polynomial and its derivative
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: A STABILITY VERSION OF THE GAUSS–LUCAS THEOREM AND APPLICATIONS