On Dirichlet Series, Fourier Series and Functional Equations
by
Eugenio P. Balanzario
UNAM-Morelia

We prove a functional equation for the Mellin transform of a periodic Fourier series. As a first application we obtain a new proof of the functional equation for the general periodic Dirichlet series. We also produce Dirichlet series, which like a famous example of Davenport and Heilbronn, satisfy functional equations and have zeros off the critical line.

Date received: January 13, 2000