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Journal of the London Mathematical Society 1993 s2-48(3):500-514; doi:10.1112/jlms/s2-48.3.500
© 1993 by London Mathematical Society
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© Oxford University Press

Proof of a Conjecture of Hayman Concerning f and f''

J. K. Langley

Department of Mathematics, University of Nottingham, University Park Nottingham NG7 2RD

We prove the following, which confirms a conjecture of W. K. Hayman from 1959. If f is meromorphic in the plane such that f and f'' have only finitely many zeros, then f(Z) = R(z) exp (P(Z)), where R is rational and P is a polynomial. The theorem is related to earlier results of Frank, Mues and others.


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