Abstract
We prove a simple form of the converse theorem for GL(n) over a function field F, “simple” referring to a cuspidal component. Thus a generic admissible irreducible representation π of the adèle group GL(\(n, \mathbb{A}\)) with cuspidal components at a finite nonempty set S of places of F whose product L-function L(t, π ×π′) is a polynomial in t and has a functional equation for each cuspidal representation π′ of GL(\(n - 1, \mathbb{A}\)) whose components at S are cuspidal, is automorphic, necessarily cuspidal. The usual form of the converse theorem deals with the case where S is empty. But our simple form is sufficient for applications of the simple trace formula.
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Flicker, Y.Z. (2013). Simple Converse Theorem. In: Drinfeld Moduli Schemes and Automorphic Forms. SpringerBriefs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5888-3_13
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