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.

URL: http://www.acadsci.fi/mathematica/Vol34/Nicks.html

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.

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About

• Item ORO ID
• 22682
• Item Type
• Journal Item
• ISSN
• 1239-629X
• Keywords
• Meromorphic function; Nevanlinna deficiency; singularities; inverse function
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2009 by Academia Scientiarum Fennica
• Depositing User
• Daniel Nicks