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Geometric zeta-functions of locally symmetric spaces

Anton Deitmar
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Abstract

The theory of geometric zeta functions for locally symmetric spaces as initialized by Selberg and continued by numerous mathematicians is generalized to the case of higher rank spaces. We show analytic continuation, describe the divisor in terms of tangential cohomology and in terms of group cohomology which generalizes the Patterson conjecture. We also extend the range of zeta functions in considering higher dimensional flats.

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Anton Deitmar. 1997-04-21. Geometric zeta-functions of locally symmetric spaces. https://arxiv.org/abs/dg-ga/9511006

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