On the type of delta-subharmonic functions of generalized refined order

In function theory, the Lindelöf theorem on zeros of entire functions is well known: A given sequence is the set of zeros of an entire function of finite order $\varrho>0$ and normal type if and only if for noninteger $\varrho$, it has a finite upper density at this order, and for integer $\varrho$, it possesses, in addition, a certain asymptotic symmetry. In this paper, we give a review of recent results relating to the extension of Lindelf̈ theorem to the case of entire functions that are analytic in the half-plane and meromorphic and subharmonic functions in the complex plane and half-plane whose is determined by the generalized refined order. Similar statements are proved for delta-subharmonic functions in the complex plane. The resulting criteria are formulated in terms of the Riesz measure functions.