Analytic Torsion, Dynamical Zeta Function, and the Fried Conjecture for Admissible Twists
نویسندگان
چکیده
We show an equality between the analytic torsion and absolute value at zero of Ruelle dynamical zeta function on a closed odd dimensional locally symmetric space twisted by acyclic flat vector bundle obtained restriction representation underlying Lie group. This generalises author’s previous result for unitarily bundles, results Bröcker, Müller, Wotzke hyperbolic manifolds.
منابع مشابه
Analytic Continuation of the Resolvent of the Laplacian and the Dynamical Zeta Function
Let s0 < 0 be the abscissa of absolute convergence of the dynamical zeta function Z(s) for several disjoint strictly convex compact obstacles Ki ⊂ R , i = 1, . . . , κ0, k0 ≥ 3, and let Rχ(z) = χ(−∆D − z2)−1χ, χ ∈ C∞ 0 (R ), be the cut-off resolvent of the Dirichlet Laplacian −∆D in Ω = RN \ ∪0 i=1Ki. We prove that there exists σ1 < s0 such that Z(s) is analytic for Re(s) ≥ σ1 and the cut-off r...
متن کاملDynamical zeta functions for analytic surface diffeomorphisms with dominated splitting
We consider a real-analytic compact surface diffeomorphism f , for which the tangent space over the nonwandering set Ω admits a dominated splitting. We study the dynamical determinant df (z) = exp− ∑ n≥1 z n ∑ x∈Fix ∗fn |Det (Df (x) − Id )|, where Fix fn denotes the set of fixed points of f with no zero Lyapunov exponents. By combining previous work of Pujals and Sambarino [PS1, PS2] on C surfa...
متن کاملOn the Holomorphy Conjecture for Igusa's Local Zeta Function
To a polynomial f over a p{adic eld K and a character of the group of units of the valuation ring of K one associates Igusa's local zeta function Z(s; f;), which is a meromorphic function on C. Several theorems and conjectures relate the poles of Z(s; f;) to the monodromy of f; the so{called holomorphy conjecture states roughly that if the order of does not divide the order of any eigenvalue of...
متن کاملAnalytic Surgery and Analytic Torsion
Analytic surgery, as defined in [9] and [6], is a one-parameter metric deformation of a Riemannian manifold M , which stretches M across a separating hypersurface H in a cylindrical fashion; the singular limit is a complete manifold with asymptotically cylindrical ends, M . In this paper, the analysis of [9] and [6] is used to study the behaviour of analytic torsion of unitary representations u...
متن کاملR-torsion and Zeta Functions for Analytic Anosov Flows on 3-manifolds
We improve previous results relating R-torsion, for an acyclic representation of the fundamental group, with a special value of the torsion zeta function of an analytic Anosov flow on a 3-manifold. By using the new techniques of Rugh and Fried we get rid of the unpleasent assumptions about the regularity of the invariant foliations.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2021
ISSN: ['0010-3616', '1432-0916']
DOI: https://doi.org/10.1007/s00220-021-04113-y