  We prove that an ordinary Dirichlet series with coefficients a(n)=g(n b) has
an abscissa of convergence 0 if g is an odd 1-periodic, real-analytic function
and b is Diophantine. We also show that if g is odd and has bounded variation
and b is of bounded Diophantine type r>1, then the abscissa of convergence is
smaller or equal than 1-1/r. Using a polylogarithm expansion, we prove that if
g is odd and real analytic and b is Diophantine, then the ordinary Dirichlet
series has an analytic continuation to the entire complex plane.
