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TitleAn explicit growth condition for middle-degree cuspidal cohomology of arithmetically defined quaternionic hyperbolic $n$-manifolds.
Author(s) Harald Grobner
TypeArticle in Journal
AbstractLet G/ℚ be the simple algebraic group Sp(n, 1) and Γ=Γ(N) a principal congruence subgroup of level N ≥ 3. Denote by K a maximal compact subgroup of the real Lie group G(ℝ) . Then a double quotient Γ∖G(ℝ)/K is called an arithmetically defined, quaternionic hyperbolic n-manifold. In this paper we give an explicit growth condition for the dimension of cuspidal cohomology H2ncusp(Γ∖G(ℝ)/K,E) in terms of the underlying arithmetic structure of G and certain values of zeta-functions. These results rely on the work of Arakawa (Automorphic Forms of Several Variables: Taniguchi Symposium, Katata, 1983, eds. I. Satake and Y. Morita (Birkhäuser, Boston), pp. 148, 1984).
KeywordsCohomology of arithmetic groups, Cuspidal cohomology, Cuspidal automorphic representation, Trace formula, Multiplicities
ISSN0026-9255; 1436-5081/e
URL http://link.springer.com/article/10.1007%2Fs00605-009-0112-4
JournalMonatsh. Math.
PublisherSpringer, Vienna
Translation No
Refereed No