/sci/ - Science & Math

https://arxiv.org/pdf/1809.01841.pdf
A vanishing criterion for Dirichlet series with periodic coefficients
>Tapas Chatterjee, M. Ram Murty, Siddhi Pathak
>(Submitted on 6 Sep 2018)
>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 characterization 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.