Fried's analytic torsion conjecture for negatively curved manifolds

Let (Σ,g)(\Sigma,g) be a negatively curved oriented compact Riemannian manifold of dimension n>2n>2, and let α\alpha be an acyclic unitary representation of π1(Σ)\pi_1(\Sigma). Let ζα\zeta_\alpha be the twisted dynamical zeta function and Tα(Σ)T_\alpha(\Sigma) the analytic torsion. Fried's conjecture.

ζα(0)(1)n1=Tα(Σ)2.|\zeta_\alpha(0)|^{(-1)^{n-1}}=|T_\alpha(\Sigma)|^2.

The source says this was proved for constant negative curvature and conjectured for general negatively curved manifolds; the supplied text gives no later resolution.

Sources & referencesView supporting material

Primary source

Maciej Zworski, “Mathematical Study of Scattering Resonances”, arXiv:1609.03550 (2017).

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