Dirichlet Series with Periodic Coefficients and Their Value-Distribution near the Critical Line

The class of Dirichlet series associated with a periodic arithmetical function includes the Riemann zeta-function as well as Dirichlet -functions to residue class characters. We study the value-distribution of these Dirichlet series and their analytic continuation in the neighbourhood of the critical line (which is the axis of symmetry of the related Riemann-type functional equation). In particular, for a fixed complex number , we find for an even or odd periodic the number of -points of the -factor of the functional equation, prove the existence of the mean of the values of taken at these points, show that the ordinates of these -points are uniformly distributed modulo one and apply this to show a discrete universality theorem.