On the location of critical points of polynomials

Authors:
Branko Curgus and Vania Mascioni

Journal:
Proc. Amer. Math. Soc. **131** (2003), 253-264

MSC (2000):
Primary 30C15; Secondary 26C10

Published electronically:
June 3, 2002

MathSciNet review:
1929045

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Abstract | References | Similar Articles | Additional Information

Abstract: Given a polynomial of degree and with at least two distinct roots let . For a fixed root we define the quantities and . We also define and to be the corresponding minima of and as runs over . Our main results show that the ratios and are bounded above and below by constants that only depend on the degree of . In particular, we prove that , for any polynomial of degree .

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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 Mathematics, Western Washington University, Bellingham, Washington 98225

Email:
masciov@cc.wwu.edu

DOI:
https://doi.org/10.1090/S0002-9939-02-06534-6

Keywords:
Roots of polynomials,
critical points of polynomials,
separation of roots

Received by editor(s):
July 10, 2001

Received by editor(s) in revised form:
September 4, 2001

Published electronically:
June 3, 2002

Communicated by:
N. Tomczak-Jaegermann

Article copyright:
© Copyright 2002
American Mathematical Society