Arithmetic Properties auf Automorphic Forms of Inner Forms of GL(n)

In this talk we will present new results on the arithmetic of
automorphic forms of the group GL(m,D) on a central simple division
algebra D over an arbitrary number field F. Our results are
generalizations of results obtained in the split case, i.e., D=F, by
Shimura, Harder, Waldspurger and Clozel for square-integrable automorphic
forms and also of Franke and Franke-Schwermer for general automorphic
representations. The global Jacquet-Langlands Correspondence, which was
recently developed by Badulescu and Badulescu-Renard, will be an important
tool. (This is joint work with A. Raghuram.)