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Gary, James Daniel 2014-12-16T06:18:11Z 2014-12-16T06:18:11Z 10000-01-01 1984 1984 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. Made available in DSpace on 2014-12-16T06:18:11Z (GMT). No. of bitstreams: 1 8502149.pdf: 2103854 bytes, checksum: d729a19cc4c4e158a9c9b3c85d2fcee1 (MD5) Previous issue date: 1984 Embargo set by: Seth Robbins for item 71392 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 99 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1984. http://hdl.handle.net/2142/71226 (UMI)AAI8502149 Mathematics On the Supremum of the Counting Function for the a-Values of a Meromorphic Function text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.