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On the zeros of the second derivative

Published online by Cambridge University Press:  14 November 2011

J. K. Langley
J. K. Langley
Affiliation:
Department of Mathematics, University of Nottingham, Nottingham, NG7 2RD, U.K.
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Abstract

Suppose that f is meromorphic of finite order in the plane, and that f″ has only finitely many zeros. We prove a strong estimate for the frequency of distinct poles of f. In particular, if the poles of f have bounded multiplicities, then f has only finitely many poles.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 2 , 1997 , pp. 359 - 368
Copyright
Copyright © Royal Society of Edinburgh 1997

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