Details:
Title  An explicit growth condition for middledegree cuspidal cohomology of arithmetically defined quaternionic hyperbolic $n$manifolds.  Author(s)  Harald Grobner  Type  Article in Journal  Abstract  Let 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 nmanifold. 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 zetafunctions. 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. 1–48, 1984).  Keywords  Cohomology of arithmetic groups, Cuspidal cohomology, Cuspidal automorphic representation, Trace formula, Multiplicities  ISSN  00269255; 14365081/e 
URL 
http://link.springer.com/article/10.1007%2Fs0060500901124 
Language  English  Journal  Monatsh. Math.  Volume  159  Number  4  Pages  335340  Publisher  Springer, Vienna  Year  2010  Edition  0  Translation 
No  Refereed 
No 
