If is a Dirichlet character mod k, then the Dirichlet L-function L(s, has trivial zeros at negative integer points, i.e. implies . Usually this result is proved with the aid of the functional equation for the L-function. As the functional equation is only valid for primitive characters, some additional arguments are necessary.
In this note the author gives a very short proof using the representation of L(s, by the Hurwitz zeta function (s,a). The only property of (s,a) he needs is proved by replacing z by -z in the contour integral of (s,a).