Mostova M. The logarithmic derivative of entire functions that close to polynomials

The relationships between the distribution of zeros of a zero-order entire function and regular behavior of such characteristics of its logarithmic derivative as the asymptotic, the Fourier coefficients, the convergence in L^p-metric are investigated. The necessary conditions for the existence of angular v-density for zeros of a zero-order entire function are found in terms of the behavior of its logarithmic derivative and there are shown that these conditions are not sufficient; criteria for the existence of angular v-density for zeros in some subclass of entire functions of order zero are proved; the sufficient conditions for the existence of angular v-density for zeros are obtained in terms of the Fourier coefficients and convergence in L^p-metric of the logarithmic derivative for entire functions of slowly growth.