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Journal of the London Mathematical Society 1992 s2-45(2):243-254; doi:10.1112/jlms/s2-45.2.243
© 1992 by London Mathematical Society
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© Oxford University Press

A Sharp Form of the Lemma on the Logarithmic Derivative

Joseph Miles

Department of Mathematics University of Illinois 1409 West Green Street Urbana Illinois 61801 USA

Let f be meromorphic in {z:|z| < R ≤ {infty}}. Upper bounds for


Formula

valid for all r < R not in a small exceptional set are obtained when R = 1 and R = {infty} . In both cases it is shown by example that the upper bounds derived for m(r,f' / f) are essentially best possible.


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