Automorphic hyperfunctions and period functions

Details Automorphic hyperfunctions and period functions Automorphic hyperfunctions and period functions

1995-08-02

arxiv.org/abs/math/9508202v1

J. reine angew. Math. 492 (1997) 1-39

Mathematics

Representation Theory

45 pages, LaTeX2e

Scientific paper

We consider invariant hyperfunctions associated to automorphic forms on the upper half plane. We give two interpretations of the period function of Maass forms introduced by Lewis. The first interpretation shows that the period function arises from the explicit description of a representative of the hyperfunction associated to the Maass form. Under certain conditions, automorphic forms determine cohomology classes in a cohomology group with values in the hyperfunctions with bounded support on the line. A map from hyperfunctions to holomorphic functions leads to a second, cohomological, interpretation of the period function.

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