Polyxeni Spilioti

activity

20152026

most citedTwisted Ruelle zeta function at zero for compact hyperbolic surfaces

6 citations · 15 across the 10 of their papers we have counts for

collaborators

11 papers

math.SP2026

Asymptotics of the spectral determinant of the weighted Laplacian for a sequence of compact Riemann surfaces of infinitely growing volume

Jay Jorgenson, Lejla Smajlovic, Polyxeni Spilioti

Let $(X, χ, k)$ be a triple consisting of a smooth, compact hyperbolic Riemann surface $X$ of genus $g$ , and an $m$ dimensional unitary multiplier system $χ$ of admissible weight $k$ …

math.NT2026

Twisted dynamical zeta functions and the Fried's conjecture

Polyxeni Spilioti

This is a survey article on the twisted dynamical zeta functions of Ruelle and Selberg and the Fried's conjecture. It is based on the mini-course: "Twisted Ruelle zeta function, co…

math.SP2025

Determinants of twisted Laplacians and the twisted Selberg zeta function

Jay Jorgenson, Lejla Smajlovic, Polyxeni Spilioti

Let $X$ be an orbisurface, meaning a compact hyperbolic Riemann surface possibly with a finite number of elliptic points, and let $X_{1}$ denote its unit tangent bundle. We consider…

math.SP2023★ 3 cited

Resonances and residue operators for pseudo-Riemannian hyperbolic spaces

Jan Frahm, Polyxeni Spilioti

For any pseudo-Riemannian hyperbolic space $X$ over $R, C, H$ or $O$ , we show that the resolvent $R (z) = (□ - z Id)^{- 1}$ of the Lapl…

math.SP2022★ 1 cited

On the spectrum of twisted Laplacians and the Teichmüller representation

Frédéric Naud, Polyxeni Spilioti

We consider Laplacians with non unitary twists acting on sections of flat vector bundles over compact hyperbolic surfaces. These non self-adjoint Laplacians have discrete spectrum…

math.SP2021★ 1 cited

The twisted Ruelle zeta function on compact hyperbolic orbisurfaces and Reidemeister-Turaev torsion

Léo Bénard, Jan Frahm, Polyxeni Spilioti

Let $X$ be a compact hyperbolic surface with finite order singularities, $X_{1}$ its unit tangent bundle. We consider the Ruelle zeta function $R (s; ρ)$ associated to a representation…

math.SP2021★ 6 cited

Twisted Ruelle zeta function at zero for compact hyperbolic surfaces

Jan Frahm, Polyxeni Spilioti

Let $X$ be a compact, hyperbolic surface of genus $g \geq 2$ . In this paper, we prove that the twisted Selberg and Ruelle zeta functions, associated with an arbitrary, finite-dimens…

math.SP2020

Twisted Ruelle zeta function on hyperbolic manifolds and complex-valued analytic torsion

Polyxeni Spilioti

In this paper, we study the twisted Ruelle zeta function associated with the geodesic flow of a compact, hyperbolic, odd-dimensional manifold $X$ . The twisted Ruelle zeta function…

math.SP2015

Functional equations of Selberg and Ruelle zeta functions for non-unitary twists

Polyxeni Spilioti

We consider the dynamical zeta functions of Selberg and Ruelle associated with the geodesic flow on a compact odd-dimensional hyperbolic manifold. These dynamical zeta functions ar…

math.SP2015★ 1 cited

Twisted Dirac operators and dynamical zeta functions

Polyxeni Spilioti

In this paper, we consider the dynamical zeta functions of Ruelle and Selberg associated with the geodesic flow of a compact hyperbolic odd dimensional manifold $X$ . These function…

math.SP2015★ 3 cited

Ruelle and Selberg zeta functions for non-unitary twists

Polyxeni Spilioti

In this paper, we study the Selberg and Ruelle zeta functions on compact hyperbolic odd dimensional manifolds. These zeta functions are defined on one complex variable $s$ in some…