  In the study of Dirichlet series with arithmetic significance there has
appeared (through the study of known examples) certain expectations, namely (i)
if a functional equation and Euler product exists, then it is likely that a
type of Riemann hypothesis will hold, (ii) that if in addition the function has
a simple pole at the point s=1, then it must be a product of the Riemann
zeta-function and another Dirichlet series with similar properties, and (iii)
that a type of converse theorem holds, namely that all such Dirichlet series
can be obtained by considering Mellin transforms of automorphic forms
associated with arithmetic groups.
