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Licensed Unlicensed Requires Authentication Published by De Gruyter May 24, 2012

Eisenstein series, cohomology of arithmetic groups, and automorphic L-functions at half integral arguments

Neven Grbac and Joachim Schwermer
From the journal Forum Mathematicum

Abstract

The automorphic cohomology of a reductive 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. The subspace spanned by all possible residues and principal values of derivatives of Eisenstein series, attached to cuspidal automorphic forms π on the Levi factor of proper parabolic ℚ-subgroups of G, forms the Eisenstein cohomology which is a natural complement to the cuspidal cohomology. We show that non-trivial Eisenstein cohomology classes can only arise if the point of evaluation features a `half-integral' property. Consequently, only the analytic behavior of the automorphic L-functions at half-integral arguments matters whether an Eisenstein series attached to a globally generic π gives rise to a residual class or not.

Funding source: FWF Austrian Science Fund

Award Identifier / Grant number: P 21090-N13

Received: 2012-4-21
Published Online: 2012-5-24
Published in Print: 2014-11-1

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