Asian Journal of Mathematics

Volume 19 (2015)

Number 1

Approximate converse theorem

Pages: 17 – 44



Min Lee (Department of Mathematics, Brown University, Providence, Rhode Island, U.S.A.)


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

Published 12 February 2015