ABSTRACT
Introduction. Nevanlinna's Value Distribution Theory and Proximity Property of a-points study, respectively, the numbers and mutual locations of a-points of arbitrary meromorphic functions in C. The main conclusion of the Theory and the Property is 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 Complex Analysis since many known classes of functions do have "slow growth", (among them classes of Bounded Functions, Hp, Dirichlet, Blaschke Products etc.). In this chapter, 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 the above results related to T-lines.
