Canad. Math. Bull. 48(2005), 321-332
Printed: Sep 2005
We study the non-vanishing on the line $Re(s)=1$ of the
convolution series associated to
two Dirichlet series in a certain class of Dirichlet series.
The non-vanishing of various $L$-functions on the line $Re(s)=1$
will be simple corollaries of our general theorems.