|Abstract:||The spectral decomposition of the space of square-integrable
automorphic forms is an important problem in the arithmetic theory of
automorphic forms on the adelic points of a (connected) reductive
algebraic group defined over a number field. The geometric importance of
the space of all automorphic forms is seen from their relation to the
cohomology of arithmetic (congruence) subgroups. In approaching both
problems the Eisenstein series play one of the key roles. We
would like to explain here some recent results in both directions.
Although essentially of different nature, the common ground for these
results is the study of analytic properties of Eisenstein series.