Asian Journal of Mathematics

Volume 19 (2015)

Number 1

Approximate converse theorem

Pages: 17 – 44

DOI: http://dx.doi.org/10.4310/AJM.2015.v19.n1.a2

Author

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

Abstract

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.

Keywords

automorphic representations, Hecke-Maass forms

2010 Mathematics Subject Classification

11F03, 11F66, 11M41

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Published 12 February 2015