On the growth of meromorphic functions with several deficient values.

Abstract

In this paper, we investigate the possibility of proving analogous theorems for meromorphic functions possessing deficient values (in the sense of R. Nevanlinna). The main interest of the results obtained lies in the fact that they provide partial answers to the three following questions. I. Under which conditions are deficiencies invariant under a change of origin? II. When are deficient values also asymptotic values? III. How does the presence of deficient values influence the gap structure of the Taylor expansion of an entire function? We leave aside questions II and III which will be treated in another paper [1]. We explain our notations in ?1 before stating our results in ?2. 1. Terminology and notations. The complex variable will be denoted by