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

Dirichlet Series with Periodic Coefficients and their Value-Distribution Near the Critical Line