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Secondary invariants and the singularity of the Ruelle zeta-function in the central critical point


Author: Andreas Juhl
Journal: Bull. Amer. Math. Soc. 32 (1995), 80-87
MSC: Primary 58F17; Secondary 11F72, 58F20
MathSciNet review: 1284776
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Abstract: The Ruelle zeta-function of the geodesic flow on the sphere bundle $ S(X)$ of an even-dimensional compact locally symmetric space X of rank 1 is a meromorphic function in the complex plane that satisfies a functional equation relating its values in s and -s. The multiplicity of its singularity in the central critical point s = 0 only depends on the hyperbolic structure of the flow and can be calculated by integrating a secondary characteristic class canonically associated to the flow-invariant foliations of $ S(X)$ for which a representing differential form is given.


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DOI: http://dx.doi.org/10.1090/S0273-0979-1995-00570-7
Article copyright: © Copyright 1995 American Mathematical Society