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

The class of Dirichlet series associated with a periodic arithmetical function $$f$$ includes the Riemann zeta-function as well $$L$$ -functions to residue characters. We study value-distribution these $$L(s;f)$$ and their analytic continuation in neighbourhood critical line (which is axis symmetry related Riemann-type functional equation). In particular, for fixed complex number $$a\neq 0$$ , we find an even or odd $$a$$ -points $$\Delta$$ -factor equation, prove existence mean values taken at points, show that ordinates are uniformly distributed modulo one apply this discrete universality theorem.