Modular representations of \(\text{PGL}_ 2\) and automorphic forms for Shimura curves. (English) Zbl 0806.11027

Let \(k\) be a local field. In this beautiful paper the author studies certain infinite dimensional representations constructed by Morita for \(\text{GL}_ 2 (k)\) via his integral theory of modular forms on the algebraic upper half plane (in particular, the theory of the “\(p\)-adic Poisson kernel”). Applications are then given to \(p\)-adic properties of modular forms on Shimura curves.


11F70 Representation-theoretic methods; automorphic representations over local and global fields
11F33 Congruences for modular and \(p\)-adic modular forms
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