Dirichlet series with periodic coefficients

In this paper we shall unify the results obtained so far in various scattered literature, for Dirichlet characters and the associated Dirichlet L-functions, under the paradigm of periodic arithmetic functions and the associated Dirichlet series. Notably we shall determine the Laurent coefficients of the series in question to cover Funakura’s result and proceed on to prove the Ayoub-Berndt-Carlitz-Chowla-Müller-Redmond theorem.