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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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Logarithm map for groups defined over adelic ring

I've been reading the book Eisenstein series and automorphic representations and I am struggling to understand the definition of a logarithm map $H:G(\mathbb{A})\rightarrow \mathfrak{h}(\mathbb{R})$ ( …
Ji Woong Park's user avatar