University of Illinois Urbana-Champaign

On the Supremum of the Counting Function for the a-Values of a Meromorphic Function

Gary, James Daniel

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https://hdl.handle.net/2142/71226

Description

Title
On the Supremum of the Counting Function for the a-Values of a Meromorphic Function
Author(s)
Gary, James Daniel
Issue Date
1984
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Abstract
  • In this dissertation two results are proved concerning the distribution of the solutions of the equation f(z) = a where f is meromorphic in the plane.
  • Letting n(r) and A(r) be the maximum and average, respectively, of the number of solutions of f(z) = a in (VBAR)z(VBAR) 0.
  • If B is a finite set of extended complex numbers and
  • (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI)
  • we show
  • for some absolute constant (beta) < e and all meromorphic f.
  • These results complement earlier results on n(r,a) obtained by Hayman and Stewart, and Toppila.
Graduation Semester
1984
Type of Resource
text
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http://hdl.handle.net/2142/71226

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