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On a conjecture of Fuchs

Published online by Cambridge University Press:  12 July 2007

Joseph Miles  and
John Rossi
Joseph Miles
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801, USA (joe@math.uiuc.edu)
John Rossi
Affiliation:
Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA (rossi@math.vt.edu)
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Abstract

If f is an entire function of order ρ, 0 < ρ < 2−11, it is shown that the Nevanlinna deficiency d(0, f′/f) of the logarithmic derivative of f satisfies For small positive ρ, this result strengthens an earlier estimate of Eremenko et al. concerning a conjecture of Fuchs.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 131 , Issue 5 , October 2001 , pp. 1209 - 1216
Copyright
Copyright © Royal Society of Edinburgh 2001

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