Information on the thesis

In the thesis 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[0; 2π]-metric are investigated. In particular, the

necessary conditions for the existence of angular υ-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 υ-density for zeros in

some subclass of entire functions of order zero are proved in terms of the

asymptotic behavior of its logarithmic derivative F, regular growth of

the Fourier coefficients of F, convergence of F by p-norm in the space

L^p[0; 2π]; the sufficient conditions for the existence of angular υ-density

for zeros are obtained for the whole class of entire functions of slowly

growth in terms of the Fourier coefficients and convergence L^p[0; 2π]–

metric of the logarithmic derivative of these functions.

Key words: entire function, zero order, angular density of zeros,

logarithmic derivative, Fourier coefficients, regular growth in L^p[0; 2π]–

metric.