The semiclassical zeta function for geodesic flows on negatively curved manifolds

Frédéric Faure, Masato Tsujii

    Research output: Contribution to journalArticlepeer-review

    32 Citations (Scopus)

    Abstract

    We consider the semi-classical (or Gutzwiller–Voros) zeta functions for C contact Anosov flows. Analyzing the spectra of the generators of some transfer operators associated to the flow, we prove that, for arbitrarily small τ> 0 , its zeros are contained in the union of the τ-neighborhood of the imaginary axis, | R(s) | < τ, and the half-plane R(s) < - χ0+ τ, up to finitely many exceptions, where χ0> 0 is the hyperbolicity exponent of the flow. Further we show that the density of the zeros along the imaginary axis satisfy an analogue of the Weyl law.

    Original languageEnglish
    Pages (from-to)851-998
    Number of pages148
    JournalInventiones Mathematicae
    Volume208
    Issue number3
    DOIs
    Publication statusPublished - Jun 1 2017

    All Science Journal Classification (ASJC) codes

    • General Mathematics

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