Convergence in $L^p[0,2\pi]$-metric of logarithmic derivative and angular $\upsilon$-density for zeros of entire function of slowly growth

Abstract

The subclass of a zero order entire function $f$ is pointed out for which the existence of angular $\upsilon$-density for zeros of entire function of zero order is equivalent to convergence in $L^p[0,2\pi]$-metric of its  logarithmic derivative.