On congruence modules related to Hilbert Eisenstein series

Transition exercise on Eisenstein series

[1] Despite occasional contrary assertions in the literature, rewriting Eisenstein series, as opposed to more general automorphic forms, to make sense on adele groups is not about Strong Approximation. Strong Approximation does make precise the relation between general automorphic forms on adele groups and automorphic forms on SLn, but rewriting these Eisenstein series does not need this compar...

Eisenstein Series*

group GC defined over Q whose connected component G 0 Q has no rational character. It is also necessary to suppose that the centralizer of a maximal Q split torus of G0C meets every component of GC. The reduction theory of Borel applies, with trivial modifications, to G; it will be convenient to assume that Γ has a fundamental set with only one cusp. Fix a minimal parabolic subgroup P 0 C defin...

A Remark on Eisenstein Series

The theory of Eisenstein series is fundamental for the spectral theory of automorphic forms. It was first developed by Selberg, and was completed by Langlands ([Lan76]; see also [MW95]). There are several known proofs for the meromorphic continuation of Eisenstein series (apart from very special cases of Eisenstein series which can be expressed in terms of Tate integrals). In all these proofs i...

*-frames for operators on Hilbert modules

$K$-frames which are generalization of frames on Hilbert spaces‎, ‎were introduced‎ ‎to study atomic systems with respect to a bounded linear operator‎. ‎In this paper‎, ‎$*$-$K$-frames on Hilbert $C^*$-modules‎, ‎as a generalization of $K$-frames‎, ‎are introduced and some of their properties are obtained‎. ‎Then some relations‎ ‎between $*$-$K$-frames and $*$-atomic systems with respect to a...

Dynamical Systems on Hilbert C*-Modules