Approximate Converse Theorem

Details Approximate Converse Theorem Approximate Converse Theorem

2012-03-28

arxiv.org/abs/1203.6328v1

Mathematics

Number Theory

Scientific paper

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.

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