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The Number of Zeros of a Polynomial in a Half-Plane

Published online by Cambridge University Press:  24 October 2008

A. Talbot
A. Talbot
Affiliation:
Imperial CollegeLondon
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Extract

The determination of the number of zeros of a complex polynomial in a half-plane, in particular in the upper and lower, or right and left, half-planes, has been the subject of numerous papers, and a full discussion, with many references, is given in Marden (l) and Wall (2), where the basis for the determination is a continued-fraction expansion, or H.C.F. algorithm, in terms of which the number of zeros in one of the half-planes can be written down at once. In addition, determinantal formulae for the relevant elements of the algorithm can be obtained, and these lead to determinantal criteria for the number of zeros, including that of Hurwitz (3) for the right and left half-planes.

Type
Articles
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 56 , Issue 2 , April 1960 , pp. 132 - 147
Copyright
Copyright © Cambridge Philosophical Society 1960

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References

REFERENCES

(1)Marden, M., The geometry of the zeros of a polynomial in a complex variable (New York, 1949), Ch. IX.Google Scholar
(2)Wall, H. S., Analytic theory of continued fractions (New York, 1948), Ch. X.Google Scholar
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