On Eisenstein series and the cohomology of arithmetic groups

On Eisenstein series and the cohomology of arithmetic groups

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Joachim Schwermer, University of Vienna, The Erwin Schrödinger International Institute for Mathematical Physics
IAS Room S-101

The automorphic cohomology of a reductive $\mathbb{Q}$--group $G$, defined in terms of the automorphic spectrum of $G$, captures essential analytic aspects of the arithmetic subgroups of $G$ and their cohomology. We discuss the actual construction of cohomology classes represented by residues or principal values of derivatives of Eisenstein series, We show that non--trivial Eisenstein cohomology classes can only arise if the point of evaluation features a 'half--integral' property. This rises questions concerning the analytic behavior of certain automorphic L--functions at half--integral arguments.