On Schlömilch series associated¶with certain Dirichlet series

Abstract:

In this paper we prove that the Dirichlet series , where a(n) is a quasi-polynomial and a, b are distinct non negative rational numbers, is, in a left half plane, a finite sum of Schlömilch-type series. As a worthwhile application we get the value at positive integers of the Hurwitz double zeta-function , , , as well as some information on L(s;a)' real zeros.