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cohomology of arithmetic groups, parabolic subgroups and the special values of $l$-functions on gl$_{n}$

Published online by Cambridge University Press:  28 July 2005

joachim mahnkopf
joachim mahnkopf
Affiliation:
institut für mathematik, universität wien, nordbergstrasse 15, 1090 wien, austria (joachim.mahnkopf@univie.ac.at)
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Abstract

let $\pi$ be a cuspidal automorphic representation of $\mathrm{gl}_n(\mathbb{a}_{\mathbb{q}})$ with non-vanishing cohomology. under a certain local non-vanishing assumption we prove the rationality of the values of the automorphic $l$-function attached to $\pi$ at critical points. conjecturally, any motivic $l$-function coincides with an $l$-function attached to an automorphic representation on $\mathrm{gl}_n$, hence, our result corresponds to a conjecture of deligne on critical values of motivic $l$-functions.

Keywords

automorphic representations and $l$-functionseisenstein seriescohomology of arithmetic groupsprimary 14g3511f1111y40
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 4 , Issue 4 , October 2005 , pp. 553 - 637
Copyright
2005 cambridge university press

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