Cohomological Theory of Dynamical Zeta Functions

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The periodic orbits of the geodesic flow of compact locally symmetric spaces of negative curvature give rise to meromorphic zeta functions. This book treats various aspects of the idea to understand the analytical properties of these zeta functions on the basis of appropriate analogues of the Lefschetz fixed point formula in which the periodic orbits of the flow take the place of the fixed points. The work analyzes the state of the research in the field of zeta functions, on the cutting edge of global analysis, harmonic analysis and dynamical systems. It connects zeta functions with index theory, geometric quantization methods, foliation theory, and representation theory.