An explicit growth condition for middle-degree cuspidal cohomology of arithmetically defined quaternionic hyperbolic n-manifolds

作者：Grobner Harald^*

来源：Monatshefte fur Mathematik, 2010, 159(4): 335-340.

DOI：10.1007/s00605-009-0112-4

• Cohomology of arithmetic groups
• Cuspidal cohomology
• Cuspidal automorphic representation
• Trace formula
• Multiplicities

Let G/Q be the simple algebraic group Sp(n, 1) and Gamma = Gamma(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 Gamma\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 H(cusp)(2n)(Gamma\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 (Birkhauser, Boston), pp. 1-48, 1984).

• 出版日期2010-3