Spectral distribution of twisted laplacian on typical hyperbolic surfaces of high genus

Y Gong - Communications in Mathematical Physics, 2024 - Springer
We investigate the spectral distribution of the twisted Laplacian associated with uniform
square-integrable bounded harmonic 1-form on typical hyperbolic surfaces of high genus …

Meromorphic continuation of Selberg zeta functions with twists having non-expanding cusp monodromy

K Fedosova, A Pohl - Selecta Mathematica, 2020 - Springer
We initiate the study of Selberg zeta functions Z_ Γ, χ Z Γ, χ for geometrically finite Fuchsian
groups Γ Γ and finite-dimensional representations χ χ with non-expanding cusp monodromy …

Complex valued analytic torsion and dynamical zeta function on locally symmetric spaces

S Shen - International Mathematics Research Notices, 2023 - academic.oup.com
We show that the Ruelle dynamical zeta function on a closed odd dimensional locally
symmetric space twisted by an arbitrary flat vector bundle has a meromorphic extension to …

Analytic torsion, dynamical zeta function, and the Fried conjecture for admissible twists

S Shen - Communications in Mathematical Physics, 2021 - Springer
We show an equality between the analytic torsion and the absolute value at zero of the
Ruelle dynamical zeta function on a closed odd dimensional locally symmetric space twisted …

[HTML][HTML] Twisted Ruelle zeta function at zero for compact hyperbolic surfaces

J Frahm, P Spilioti - Journal of Number Theory, 2023 - Elsevier
Let X be an orientable compact connected hyperbolic surface of genus g. In this paper, we
prove that the twisted Selberg and Ruelle zeta functions, associated with an arbitrary finite …

Ruelle zeta functions of hyperbolic manifolds and Reidemeister torsion

W Müller - The Journal of Geometric Analysis, 2021 - Springer
This paper is concerned with the behavior of twisted Ruelle zeta functions of compact
hyperbolic manifolds at the origin. Fried proved that for an orthogonal acyclic representation …

Fourier expansions of vector-valued automorphic functions with non-unitary twists

K Fedosova, A Pohl, J Rowlett - arXiv preprint arXiv:2201.04454, 2022 - arxiv.org
We provide Fourier expansions of vector-valued eigenfunctions of the hyperbolic Laplacian
that are twist-periodic in a horocycle direction. The twist may be given by any endomorphism …

On Fried's conjecture for compact hyperbolic manifolds

W Mueller - arXiv preprint arXiv:2005.01450, 2020 - arxiv.org
Fried's conjecture is concerned with the behavior of dynamical zeta functions at the origin.
For compact hyperbolic manifolds, Fried proved that for an orthogonal acyclic representation …

Reidemeister torsion, complex volume and the Zograf infinite product for hyperbolic 3–manifolds

J Park - Geometry & Topology, 2019 - msp.org
Reidemeister torsion, complex volume and the Zograf infinite product for hyperbolic 3–manifolds
Page 457 msp Geometry & Topology 23 (2019) 3687–3734 Reidemeister torsion, complex …

The spectral concentration for damped waves on compact Anosov manifolds

Y Gong - arXiv preprint arXiv:2411.02929, 2024 - arxiv.org
We study the spectral distribution of damped waves on compact Anosov manifolds. Sj\"
ostrand\cite {SJ1} proved that the imaginary parts of the majority of the eigenvalues …