Twisted Ruelle zeta function at zero for compact hyperbolic surfaces

Jan Frahm; Polyxeni Spilioti

doi:10.1016/j.jnt.2022.08.003

Twisted Ruelle zeta function at zero for compact hyperbolic surfaces

Jan Frahm^*, Polyxeni Spilioti

^*Corresponding author af dette arbejde

Institut for Matematik

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

3 Citationer (Scopus)

Abstract

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-dimensional complex representation χ of π ₁(X) admit a meromorphic continuation to C. Moreover, we study the behavior of the twisted Ruelle zeta function at s=0 and prove that at this point it has a zero of order dim⁡(χ)(2g−2).

Originalsprog	Engelsk
Tidsskrift	Journal of Number Theory
Vol/bind	243
Sider (fra-til)	38-61
Antal sider	24
ISSN	0022-314X
DOI	https://doi.org/10.1016/j.jnt.2022.08.003
Status	Udgivet - feb. 2023

Adgang til dokumentet

10.1016/j.jnt.2022.08.003Licens: CC BY

https://arxiv.org/abs/2105.13321

Symmetry Breaking in Mathematics
Frahm, J. (PI), Weiske, C. (Deltager), Ditlevsen, J. (Deltager), Spilioti, P. (Deltager), Bang-Jensen, F. J. (Deltager) & Labriet, Q. (Deltager)
01/08/2019 → 31/07/2024
Projekter: Projekt › Forskning

Citationsformater

@article{5574798c11c643e6a47d124b6343e441,

title = "Twisted Ruelle zeta function at zero for compact hyperbolic surfaces",

abstract = "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-dimensional complex representation χ of π 1(X) admit a meromorphic continuation to C. Moreover, we study the behavior of the twisted Ruelle zeta function at s=0 and prove that at this point it has a zero of order dim⁡(χ)(2g−2).",

keywords = "Non-unitary representations, Selberg trace formula, Twisted Ruelle zeta function, Twisted Selberg zeta function",

author = "Jan Frahm and Polyxeni Spilioti",

year = "2023",

month = feb,

doi = "10.1016/j.jnt.2022.08.003",

language = "English",

volume = "243",

pages = "38--61",

journal = "Journal of Number Theory",

issn = "0022-314X",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Twisted Ruelle zeta function at zero for compact hyperbolic surfaces

AU - Frahm, Jan

AU - Spilioti, Polyxeni

PY - 2023/2

Y1 - 2023/2

N2 - 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-dimensional complex representation χ of π 1(X) admit a meromorphic continuation to C. Moreover, we study the behavior of the twisted Ruelle zeta function at s=0 and prove that at this point it has a zero of order dim⁡(χ)(2g−2).

AB - 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-dimensional complex representation χ of π 1(X) admit a meromorphic continuation to C. Moreover, we study the behavior of the twisted Ruelle zeta function at s=0 and prove that at this point it has a zero of order dim⁡(χ)(2g−2).

KW - Non-unitary representations

KW - Selberg trace formula

KW - Twisted Ruelle zeta function

KW - Twisted Selberg zeta function

U2 - 10.1016/j.jnt.2022.08.003

DO - 10.1016/j.jnt.2022.08.003

M3 - Journal article

SN - 0022-314X

VL - 243

SP - 38

EP - 61

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

Twisted Ruelle zeta function at zero for compact hyperbolic surfaces

Abstract

Adgang til dokumentet

Fingeraftryk

Projekter

Symmetry Breaking in Mathematics

Citationsformater