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Title:On the Supremum of the Counting Function for the a-Values of a Meromorphic Function
Author(s):Gary, James Daniel
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(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
(DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI)
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.
Issue Date:1984
Type:Text
Description:99 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1984.
URI:http://hdl.handle.net/2142/71226
Other Identifier(s):(UMI)AAI8502149
Date Available in IDEALS:2014-12-16
Date Deposited:1984


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