\Gamma-lines approach in the theory of meromorphic function
by
Grigor Barsegian
Institute of Mathematics of Acad. of Sci. of Armenia

The R. Nevanlinna's Value Distribution Theory and Proximity Property of a-points study respectively numbers and mutual locations of a-points of arbitrary meromorphic functions in C. The main conclusion of the Theory and the Property are true also for meromorphic functions with ''fast growth'' in the unit disk, but not for functions with ''slow growth'' in general. The last circumstance is an essential gap in the Complex Analysis since many known classes of functions do have ''slow growth'', (among them classes of Bounded Functions, H^p, Dirichlet, Blaschke Products etc.). In this talk we offer a novel, geometric approach to the study of Value Distribution and mutual locations of a-points for arbitrary meromorphic functions including those with slow growth. Our approach is based on results related to the \Gamma-lines.

Date received: July 30, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahv-99.