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A Bound for the Moduli of the Zeros of Polynomials

Published online by Cambridge University Press:  20 November 2018

Q. I. Rahman
Q. I. Rahman*
Affiliation:
Université de Montréal, Montréal, Québec
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The following theorem is due to Walsh [2]. For another proof see [1].

Theorem A. All the zeros of the polynomial p(z) = a0 + a1z + … an-1zn-1+zn lie on the disk.

where M = Σj = 2n|an-j|1/j

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 4 , December 1970 , pp. 541 - 542
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Bell, H. E., Gershgorirfs theorem and the zeros of polynomials, Amer. Math.Monthly, 72 (1965), 292-295.Google Scholar
2. Walsh, J. L., An inequality for the roots of an algebraic equation, Ann. of. Math. 25 (1924), 285-286.Google Scholar