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Proof of a Conjecture of Hayman Concerning f and f ″
Author(s) -
Langley J. K.
Publication year - 1993
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-48.3.500
Subject(s) - meromorphic function , conjecture , mathematics , polynomial , complex plane , finitely generated abelian group , plane (geometry) , combinatorics , pure mathematics , discrete mathematics , mathematical analysis , geometry
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.