Approximate converse theorem

The theme of this thesis is an "approximate converse theorem" for globally unramified cuspidal representations of PGL(n, A), n ≥ 1. For a given set of Langlands parameters for some places of Q, we can compute ε > 0 such that there exists a genuine globally unramified cuspidal representation, whose Langlands parameters are within ε of the given ones for finitely many places.