On Dirichlet series with periodic coefficients

We investigate Dirichlet series L(s, f) = Sigma(n=1)(infinity)f(n)/n(s) with q-periodic coefficients f(n), i.e. f(n+q) = f(n) for all integers n and some fixed integer q, and we prove an asymptotic formula for the number of nontrivial zeros of L(s, f). Further, we give a necessary condition for L(s, f) to have a distribution of the nontrivial zeros symmetrical with respect to the critical line.