Sokulska N. The properties of meromorphic functions in a half-strip

The relations for the Fourier coefficients of the logarithm modulus of meromorphic function in the closure of the rectangle are investigated, which helped to formulate and prove a criterion of lambda - type finiteness of holomorphic in the half-strip functions and describe the zero sets of holomorphic and zero and pole sets of meromorphic functions f of finite lambda - type with arbitrary restrictions on their growth characteristics. The asymptotic for Nevanlinna characteristic of loxodromic functions is obtained. A value distribution theorem for functions from classes of multiplicatively periodic meromorphic functions in the punctured closure of the upper half-plane is proved.