On the Type of Subharmonic Functions of Finite Order

Abstract

Theorems establishing a connection between the type of an entire function and the distribution of its zeros play an important role in the theory of entire functions. The classical Lindelöf theorem asserts that zeros of an entire function of finite integer order and normal type possess a certain symmetry property. We prove counterparts of the Lindelöf theorem in the spaces of subharmonic functions in the complex plane and in the half-plane the growth of which is determined by the proximate order in the sense of Boutroux. The results are formulated in the terms of the upper density and the upper balance of the Riesz measure and the full measure of functions.