Asian Journal of Mathematics
Volume 19 (2015)
Approximate converse theorem
Pages: 17 – 44
We present an approximate converse theorem which measures how close a given set of irreducible admissible unramified unitary generic local representations of $GL(n)$ is to a genuine cuspidal representation. To get a formula for the measure, we introduce a quasi-Maass form on the generalized upper half plane for a given set of local representations. We also construct an annihilating operator which enables us to write down an explicit cuspidal automorphic function.
automorphic representations, Hecke-Maass forms
2010 Mathematics Subject Classification
11F03, 11F66, 11M41