On the growth of meromorphic functions on rays

Abstract

In this paper I investigate the behaviour of

$$L = \lim \,\mathop {\inf }\limits_{r \to \infty } |\log |f(re^{i\delta } )| + \log |f(re^{ - i\delta } )||/N(r)$$

(1)

where f is a meromorphic function of non-integral order λ,

$$N(r) = N(r,f) + N(r,1/f)$$

and

$$0 \leqq \delta < \pi .$$

Research carried out with support by NSF grant MCS 76-0654.