Weil's converse theorem for Maass forms and cancellation of zeros

Abstract

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.

Updated introduction

References in corpus (2)

• Converse theorems for automorphic distributions and Maass forms of level N
• A converse theorem without root numbers

Cited by in corpus (2)

• Converse theorems for automorphic distributions and Maass forms of level N
• Automorphic pairs of distributions on $\mathbb{R}$, and Maass forms of real weights