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Title of Journal: Monatsh Math

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Abbravation: Monatshefte für Mathematik

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Springer Vienna

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DOI

10.1016/0769-2609(87)90206-7

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1436-5081

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An explicit growth condition for middledegree cus

Authors: Harald Grobner
Publish Date: 2009/04/07
Volume: 159, Issue: 4, Pages: 335-340
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Abstract

Let G/mathbb Q be the simple algebraic group Spn 1 and Gamma=GammaN a principal congruence subgroup of level N ≥ 3 Denote by K a maximal compact subgroup of the real Lie group Gmathbb R Then a double quotient Gammabackslash Gmathbb 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 H2n cuspGammabackslash Gmathbb R/KE 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

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Other Papers In This Journal:
  1. A central limit theorem for integer partitions
  2. Fully commutative elements in finite and affine Coxeter groups
  3. On semi-rational finite simple groups
  4. Integer-valued polynomials over matrices and divided differences
  5. On mean values of multiplicative functions on the symmetric group
  6. Simple exceptional groups of Lie type are determined by their character degrees
  7. Löwner chains with complex leading coefficient
  8. On a functional equation related to derivations in prime rings
  9. Ricci solitons and odd-dimensional spheres
  10. Regularity properties of distributions through sequences of functions
  11. Operations with monotone operators and the monotonicity of the resulting operators
  12. Normal families of meromorphic functions and shared values
  13. Some New Results on the Chu Duality of Discrete Groups
  14. Cauchy integral and singular integral operator over closed Jordan curves
  15. The zero-free region of the derivative of Selberg zeta functions
  16. A note on Engel words of finite groups
  17. Equivalence of plurisubharmonic singularities and Siu-type metrics
  18. Palindromic Prefixes and Diophantine Approximation
  19. Effective uniqueness of Parry measure and exceptional sets in ergodic theory
  20. On matrix valued square integrable positive definite functions
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