A contraction of the Lucas polygon
Authors:
Branko Curgus and Vania Mascioni
Journal:
Proc. Amer. Math. Soc. 132 (2004), 29732981
MSC (2000):
Primary 30C15; Secondary 26C10
Published electronically:
May 20, 2004
MathSciNet review:
2063118
Fulltext PDF Free Access
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Abstract: The celebrated GaussLucas theorem states that all the roots of the derivative of a complex nonconstant polynomial lie in the convex hull of the roots of , called the Lucas polygon of . We improve the GaussLucas theorem by proving that all the nontrivial roots of lie in a smaller convex polygon which is obtained by a strict contraction of the Lucas polygon of .
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Additional Information
Branko Curgus
Affiliation:
Department of Mathematics, Western Washington University, Bellingham, Washington 98225
Email:
curgus@cc.wwu.edu
Vania Mascioni
Affiliation:
Department of Mathematical Sciences, Ball State University, Muncie, Indiana 473060490
Email:
vdm@bsucs.bsu.edu
DOI:
http://dx.doi.org/10.1090/S0002993904072314
PII:
S 00029939(04)072314
Keywords:
Roots of polynomials,
critical points of polynomials,
GaussLucas theorem
Received by editor(s):
October 29, 2002
Received by editor(s) in revised form:
February 12, 2003
Published electronically:
May 20, 2004
Communicated by:
N. TomczakJaegermann
Article copyright:
© Copyright 2004
American Mathematical Society
