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Functional equations of Selberg and Ruelle zeta functions for non-unitary twists

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We consider the dynamical zeta functions of Selberg and Ruelle associated with the geodesic flow on a compact odd-dimensional hyperbolic manifold. These dynamical zeta functions are defined for a complex variable s in some right-half plane of C. In Spilioti (Ann Glob Anal Geom 53(2):151–203, 2018), it was proved that they admit a meromorphic continuation to the whole complex plane. In this paper, we establish functional equations for them, relating their values at s with those at - s. We prove also a determinant representation of the zeta functions, using the regularized determinants of certain twisted differential operators.

Original languageEnglish
JournalAnnals of Global Analysis and Geometry
Pages (from-to)35-77
Number of pages43
Publication statusPublished - 2020

    Research areas

  • Determinant formula, Dynamical zeta functions, Eta invariant, Functional equations

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