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On a conjecture of Ilieff

Published online by Cambridge University Press:  24 October 2008

D. A. Brannan
D. A. Brannan
Affiliation:
Imperial College, London
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Extract

We will here prove the following special case of an (unpublished) conjecture for a polynomial of degree ndue to L. Ilieff:

Theorem. If all zeros of the cubic polynomial p3(z) lie in |z| ≤ 1, then at least one zero of p3′(z) lies in or on the boundary of a circle of radius unity around each zero of p′3(z).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 1 , January 1968 , pp. 83 - 85
Copyright
Copyright © Cambridge Philosophical Society 1968

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References

REFERENCES

(1)Marden, M.The geometry of the zeros of a polynomial in a complex variable (New York, 1949).Google Scholar
(2)Joyal, A. (To appear.)Google Scholar