Automorphic Forms, Cohomology and CAP Representations. The Case $GL_2$ over a definite quaternion algebra

Harald Grobner

Automorphic Forms, Cohomology and CAP Representations. The Case $GL_2$ over a definite quaternion algebra

Number Theory 2011-09-28 v5

Authors: Harald Grobner

Abstract

In this paper we fully describe the cuspidal and the Eisenstein cohomology of the group $G=GL_2$ over a definite quaternion algebra $D/\Q$ . Functoriality is used to show the existence of residual and cuspidal automorphic forms, having cohomology in degree 1. The latter ones turn out to be CAP-representations, though $G$ satisfies Strong Multiplicity One. A non-vanishing result on intertwining operators of induced representations will serve as a starting point for further investigations concerning rationality of critical $L$ -values.

Keywords

automorphic forms cohomology CAP representations GL_2 quaternion algebra Eisenstein cohomology cuspidal cohomology L-values

Cite

@article{arxiv.1003.2326,
  title  = {Automorphic Forms, Cohomology and CAP Representations. The Case $GL_2$ over a definite quaternion algebra},
  author = {Harald Grobner},
  journal= {arXiv preprint arXiv:1003.2326},
  year   = {2011}
}

Comments

In (.v4) two different versions of this paper were compiled in one single file by mistake. In order to correct that I uploaded this new version

Automorphic Forms, Cohomology and CAP Representations. The Case $GL_2$ over a definite quaternion algebra

Abstract

Keywords

Cite

Comments

Related papers