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Deficiencies of certain classes of meromorphic functions

Nicks, Daniel A. (2009). Deficiencies of certain classes of meromorphic functions. Annales Academiae Scientiarum Fennicae Mathematica, 34(1) pp. 157–171.

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Abstract

Denote by B the class of transcendental meromorphic functions for which the set of finite critical and asymptotic values is bounded, and by S that class of functions for which this set is finite. We give some conditions on transcendental deficient functions of members of the class B, including an improvement of a result of Langley and Zheng. This leads to corresponding results for the class S. It is also proved that no derivative of a finite lower order periodic function has non-zero finite deficient values. We show by example that the finite lower order condition is necessary here.

Item Type: Journal Article
Copyright Holders: 2009 by Academia Scientiarum Fennica
ISSN: 1239-629X
Keywords: Meromorphic function; Nevanlinna deficiency; singularities; inverse function
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 22682
Depositing User: Daniel Nicks
Date Deposited: 05 Aug 2010 12:04
Last Modified: 27 Oct 2012 16:12
URI: http://oro.open.ac.uk/id/eprint/22682
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