On the asymptotics of the analytic torsion for compact hyperbolic orbifolds

Fedosova, Ksenia

doi:10.48550/arxiv.1511.04281

Cited by 2 publications

(4 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A difference with the results in [17,Section 8] is that the coefficients of W j γσ have oscillating factors r d γ,j . Moreover, Theorem 0.7.1 is compatible with the results of Ksenia Fedosova [30] on the asymptotics of Ray-Singer analytic torsions for compact hyperbolic orbifolds. She obtained instead the oscillating factors from the contributions of the elliptic elements in Γ, which is not assumed to be torsion-free.…”

Section: Introductionsupporting

confidence: 78%

“…In this section, we compute the asymptotics of the equivariant Ray-Singer analytic torsion associated with a certain family of flat homogeneous vector bundles on a compact locally symmetric space Z = Γ\X. We extend the results of [50], [17,Section 8] and [30].…”

Section: The Asymptotics Of the Equivariant Ray-singer Analytic Torsionmentioning

confidence: 99%

“…Here, following the ideas in [17, Section 8], we will be concerned with the asymptotics of the equivariant Ray-Singer analytic torsion for Z. A similar problem has already been considered by Ksenia Fedosova [30] using methods of harmonic analysis on the hyperbolic spaces [31]. In this paper, we will exploit instead our explicit formula for twisted orbital integrals.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Hypoelliptic Laplacian and twisted trace formula

Liu

2018

Comptes Rendus. Mathématique

View full text Add to dashboard Cite

We give an explicit geometric formula for the twisted orbital integrals using the method of the hypoelliptic Laplacian developed by Bismut. Combining with the twisted trace formula, we can evaluate the equivariant trace of the heat operators of the Laplacians on a compact locally symmetric space. As an application, we use our formula to compute the leading term in the asymptotic expansion of the equivariant analytic torsions for a compact locally symmetric space.

show abstract

Section: Introductionsupporting

confidence: 78%

Section: The Asymptotics Of the Equivariant Ray-singer Analytic Torsionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Hypoelliptic Laplacian and twisted trace formula

Liu

2018

Comptes Rendus. Mathématique

View full text Add to dashboard Cite

show abstract

“…Let us also mention Fedosova's recent work [Fe15a,Fe15b,Fe16] on the Selberg zeta function and the asymptotic behavior of the analytic torsion of unimodular flat orbifold vector bundles on hyperbolic orbifolds. 0.4.…”

Section: Introductionmentioning

confidence: 99%

Flat vector bundles and analytic torsion on orbifolds

Shen¹,

Yu²

2017

Preprint

View full text Add to dashboard Cite

This article is devoted to a study of flat orbifold vector bundles. We construct a bijection between the isomorphic classes of proper flat orbifold vector bundles and the equivalence classes of representations of the orbifold fundamental groups of base orbifolds.We establish a Bismut-Zhang like anomaly formula for the Ray-Singer metric on the determine line of the cohomology of a compact orbifold with coefficients in an orbifold flat vector bundle.We show that the analytic torsion of an acyclic unitary flat orbifold vector bundle is equal to the value at zero of a dynamical zeta function when the underlying orbifold is a compact locally symmetric space of the reductive type, which extends one of the results obtained by the first author for compact locally symmetric manifolds. CONTENTS 5.4. Semisimple orbital integral 41 5.5. Locally symmetric spaces 42 5.6. Ruelle dynamical zeta functions 44 5.7. Reductive group with δ(G) = 1 and with compact center 45 5.8. Auxiliary virtual representations of K 47 5.9. Evaluation of Tr s [γ] [exp(−tC g,X, η /2)] 47 5.10. Selberg zeta functions 50 5.11. The proof of Theorem 5.8 when G has compact center and δ(G) = 1 51 References 51

show abstract

On the asymptotics of the analytic torsion for compact hyperbolic orbifolds

Abstract: We study the analytic torsion of odd-dimensional hyperbolic orbifolds Γ\H 2n+1 , depending on a representation of Γ. Our main goal is to understand the asymptotic behavior of the analytic torsion with respect to sequences of representations associated to rays of highest weights.

Cited by 2 publications

References 9 publications

Hypoelliptic Laplacian and twisted trace formula

Hypoelliptic Laplacian and twisted trace formula

Flat vector bundles and analytic torsion on orbifolds

Contact Info

Product

Resources

About