Hostname: page-component-6bb9c88b65-k72x6 Total loading time: 0 Render date: 2025-07-22T23:44:26.355Z Has data issue: false hasContentIssue false
  • English
  • Français

On a conjecture of Ilieff

Published online by Cambridge University Press:  24 October 2008

D. A. Brannan
D. A. Brannan
Affiliation:
Imperial College, London
Get access Rights & Permissions [Opens in a new window]

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We will here prove the following special case of an (unpublished) conjecture for a polynomial of degree ndue to L. Ilieff: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

Information

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

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