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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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How to read the paper of Arthur on trace formula on general reductive groups
One of the best places to learn about trace formula, other than David Whitehouse's wonderful notes, are the notes by Erez Lapid Introductory notes on the trace formula.
Arthur's trace formula relies o …