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An automorphic form is a well-behaved function from a topological group $G$ to the complex numbers (or complex vector space) which is invariant under the action of a discrete subgroup $\Gamma \subset G$ of the topological group. Automorphic forms are a generalization of the idea of periodic functions in Euclidean space to general topological groups.

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embedding of local tempered representation into cuspidal automorphic representation

Let v be a finite place of a number field F. Let $\pi_{v}$ be an irreducible tempered representation of $ GL_{n}(F_v)$. Is it true that we can find some irreducible cuspidal automorphic representation …