Use this URL to cite or link to this record in EThOS:  http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.405162 
Title:  Analogues of Picard sets for meromorphic functions with a deficient value  
Author:  Kendall, Guy 
ISNI:
0000 0001 2442 1588


Awarding Body:  University of Nottingham  
Current Institution:  University of Nottingham  
Date of Award:  2004  
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Abstract:  
Picard's theorem states that a nonconstant function which is meromorphic in the complex plane C omits at most two values of the extended complex plane C*. A Picard set for a family of functions F is a subset E of the plane such that every transcendental f in F takes every value of C*, with at most two exceptions, infinitely often in CE. If f is transcendental and meromorphic in the plane, then: (i) [Hayman and others] if N is a positive integer, f^Nf' takes all finite nonzero values infinitely often; (ii) [Hayman] either f takes every finite value infinitely often, or each derivative f^(k) takes every finite nonzero value infinitely often. We can seek analogues of Picard sets ie subsets E of the plane and an associated family of functions F, such that (for case (i)) f^Nf' takes all finite nonzero values infinitely often in CE, for all f in F. Similarly for case (ii). In this thesis we improve or extend the results previously known, both for Picard sets proper and for the analogous cases (i) and (ii) mentioned above, when the family of functions F consists of meromorphic functions which have deficient poles (in the sense of Nevanlinna).


Supervisor:  Not available  Sponsor:  Not available  
Qualification Name:  Thesis (Ph.D.)  Qualification Level:  Doctoral  
EThOS ID:  uk.bl.ethos.405162  DOI:  Not available  
Keywords:  QA299 Analysis  
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