Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A refinement of the Gauss-Lucas theorem
HTML articles powered by AMS MathViewer

by Dimitar K. Dimitrov PDF
Proc. Amer. Math. Soc. 126 (1998), 2065-2070 Request permission

Abstract:

The classical Gauss-Lucas Theorem states that all the critical points (zeros of the derivative) of a nonconstant polynomial $p$ lie in the convex hull $\Xi$ of the zeros of $p$. It is proved that, actually, a subdomain of $\Xi$ contains the critical points of $p$.
References
  • F. Lucas, Propriétés géométriques des fractions rationnelles, C. R. Acad. Sci. Paris 77(1874), 431-433; 78(1874), 140-144; 78(1874), 180-183; 78(1874), 271-274.
  • Morris Marden, Geometry of polynomials, 2nd ed., Mathematical Surveys, No. 3, American Mathematical Society, Providence, R.I., 1966. MR 0225972
  • Morris Marden, Conjectures on the critical points of a polynomial, Amer. Math. Monthly 90 (1983), no. 4, 267–276. MR 700266, DOI 10.2307/2975758
  • G. Szegő, Bemerkungen zu einen Satz von J.H.Grace über die Wurzeln algebraischer Gleichungen, Math.Z. 13(1922), 28-55.
  • J. L. Walsh, On the location of the roots of the derivative of a polynomial, C. R. Congr. Internat. des Mathématiciens, Strasbourg, 1920, pp. 339-342.
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 30C15, 26C10
  • Retrieve articles in all journals with MSC (1991): 30C15, 26C10
Additional Information
  • Dimitar K. Dimitrov
  • Affiliation: Departamento de Ciências de Computação e Estatística, IBILCE, Universidade Estadual Paulista, 15054-000 São José do Rio Preto, SP, Brazil
  • MR Author ID: 308699
  • Email: dimitrov@nimitz.dcce.ibilce.unesp.br
  • Received by editor(s): December 29, 1996
  • Additional Notes: Research supported by the Brazilian foundation CNPq under Grant 300645/95-3 and the Bulgarian Science Foundation under Grant MM-414.
  • Communicated by: Albert Baernstein II
  • © Copyright 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 2065-2070
  • MSC (1991): Primary 30C15, 26C10
  • DOI: https://doi.org/10.1090/S0002-9939-98-04381-0
  • MathSciNet review: 1452801