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Geometric zeta functions of locally symmetric spaces
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 122, Number 5, October 2000
- pp. 887-926
- 10.1353/ajm.2000.0037
- Article
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The theory of geometric zeta functions for locally symmetric spaces is generalized to the case of higher rank spaces. We show that the zeta functions can be continued to meromorphic functions on the plane, describe the divisor in terms of tangential cohomology and in terms of group cohomology which generalizes a conjecture of Patterson. We also extend the range of zeta functions in considering higher dimensional flats.