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About a problem of Hermite and Biehler

Part of: Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  09 April 2009

Todor Stoyanov
Todor Stoyanov
Affiliation:
Economic University, Department of Mathematics, bul. Knyaz Boris I 77, Varna 9002, Bulgaria e-mail: todstoyanov@yahoo.com, library @ mail.ue-varna.bg
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Abstract

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A point of departure for this paper is the famous theorem of Hermite and Biehler: If f (z) is a polynomial with complex coefficients ak and its zeros zk satisfy Im Zk < 0, then the polynomials with coefficients Re ak, and Im ak have only real zeros.

We generalize this theorem for some entire functions. The entire functions in Theorem 2 and Theorem 3 are of first and second genus respectively.

MSC classification

Secondary: 30D20: Entire functions, general theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 72 , Issue 1 , February 2002 , pp. 87 - 92
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Pólya, G. and Szegö, G., Problems and theorems in analysis (Springer, Berlin, 1972).Google Scholar
[2]Titchmarsh, E. C., The theory of functions (Oxford Univ. Press, London, 1939).Google Scholar