On the zeros of a polynomial and its derivatives
Author:
Piotr Pawlowski
Journal:
Trans. Amer. Math. Soc. 350 (1998), 44614472
MSC (1991):
Primary 30C15
MathSciNet review:
1473453
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Abstract: If is univariate polynomial with complex coefficients having all its zeros inside the closed unit disk, then the GaussLucas theorem states that all zeros of lie in the same disk. We study the following question: what is the maximum distance from the arithmetic mean of all zeros of to a nearest zero of ? We obtain bounds for this distance depending on degree. We also show that this distance is equal to for polynomials of degree 3 and polynomials with real zeros.
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Additional Information
Piotr Pawlowski
Affiliation:
Department of Mathematics and Computer Science, Kent State University, Kent, Ohio 44242
Address at time of publication:
Summit Systems, Inc., 22 Cortland St., New York, New York 10007
Email:
piotrpawlowski@summithq.com
DOI:
http://dx.doi.org/10.1090/S0002994798022910
PII:
S 00029947(98)022910
Keywords:
Polynomials,
location of zeros
Received by editor(s):
June 27, 1996
Article copyright:
© Copyright 1998 American Mathematical Society
