Zabolots'kyj M. Asymptotic properties of analytic and subharmonic functions of non-rapid growth

We investigate conditions on the coefficients of an entire function under which the basic Nevanlinna characteristics are slowly growing functions. New approach to investigating asymptotical properties of entire functions of zero order was suggested. It is based on multinomial asymptotics of integrals. There were introduced new notions of regularity and "indicator" for entire functions of zero order we find a criterion of this regularity in terms of zeros of a function. New asymptotic representations for deltasubharmonic functions of zero genus are found. Using these representations we establish new sharp lower estimates for some supclasses of functions.