Abstract:
We address the question of non-vanishing of L(1, f) where f is an algebraic-
valued, periodic arithmetical function. We do this by characterizing algebraic-valued,
periodic functions f for which L(1, f) = 0. The case of odd functions was resolved
by Baker, Birch and Wirsing in 1973. We apply a result of Bass to obtain a charac-
terization for the even functions. We also describe a theorem of the first two authors
which says that it is enough to consider only the even and the odd functions in order
to obtain a complete characterization.
