On the zeros of a polynomial and its derivatives

Author:
Piotr Pawlowski

Journal:
Trans. Amer. Math. Soc. **350** (1998), 4461-4472

MSC (1991):
Primary 30C15

MathSciNet review:
1473453

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Abstract | References | Similar Articles | Additional Information

Abstract: If is univariate polynomial with complex coefficients having all its zeros inside the closed unit disk, then the Gauss-Lucas 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:
piotr-pawlowski@summithq.com

DOI:
http://dx.doi.org/10.1090/S0002-9947-98-02291-0

Keywords:
Polynomials,
location of zeros

Received by editor(s):
June 27, 1996

Article copyright:
© Copyright 1998
American Mathematical Society