Vorobiov Y. Distribution of values of the Hecke Z-function

The new theorem of the "density" in the problem of the distribution of zeros of Z-function was proved. The analytic continuation of Laplace transform of product of two Z-functions and for the product of Hurwitz zeta-function and Lerch zeta-function was obtained. The estimate of sumator function, that is assosiated with the function of unit devisors over the ring of integer Gaussian numbers was obtained also. There has been found an asymptotic representation on mean value of summation function for the multiplicative functions, defined by Dirichlet series with particularities on the singular line.