The distribution of the zeros of holomorphic functions of moderate growth in the unit disc and the representation of meromorphic functions there

Let be the unit disc in the complex plane  and a class of holomorphic functions in  distinguished by a restriction on their growth in a neighbourhood of the boundary of the disc which is stated in terms of weight functions of moderate growth. Some results which describe the sequences of zeros for holomorphic functions in classes  of this type are obtained. The weight functions defining  are not necessarily radial; however the results obtained are new even in the case of radial constraints. Conditions for meromorphic functions in  ensuring that they can be represented as a ratio of two functions in sharing no zeros are investigated. Bibliography: 28 titles.