  We prove two principal results. Firstly, we characterise Maass forms in terms
of functional equations for Dirichlet series twisted by primitive characters.
The key point is that the twists are allowed to be meromorphic. This weakened
analytic assumption applies in the context of our second theorem, which shows
that the quotient of the symmetric square L-function of a Maass newform and the
Riemann zeta function has infinitely many poles.
