Some results on entire functions of finite lower order

Abstract

Letf(z) be an entire function of order λ and of finite lower order μ. If the zeros off(z) accumulate in the vicinity of a finite number of rays, then (a) λ is finite; (b) for every arbitrary numberk1>1, there existsk2>1 such thatT(k1r,f)≤k2T(r,f) for allr≥r0. Applying the above results, we prove that iff(z) is extremal for Yang's inequalityp=g/2, then (c) every deficient values off(z) is also its asymptotic value; (d) every asymptotic value off(z) is also its deficient value; (e) λ=μ; (f) \(\sum\limits_{a \ne \infty } {\delta (a,f) \leqslant 1 - k(\mu ).} \)