---
_id: '31059'
abstract:
- lang: eng
  text: In this article we prove meromorphic continuation of weighted zeta functions
    in the framework of open hyperbolic systems by using the meromorphically continued
    restricted resolvent of Dyatlov and Guillarmou (2016). We obtain a residue formula
    proving equality between residues of weighted zetas and invariant Ruelle distributions.
    We combine this equality with results of Guillarmou, Hilgert and Weich (2021)
    in order to relate the residues to Patterson-Sullivan distributions. Finally we
    provide proof-of-principle results concerning the numerical calculation of invariant
    Ruelle distributions for 3-disc scattering systems.
author:
- first_name: Philipp
  full_name: Schütte, Philipp
  id: '50168'
  last_name: Schütte
- first_name: Tobias
  full_name: Weich, Tobias
  id: '49178'
  last_name: Weich
  orcid: 0000-0002-9648-6919
- first_name: Sonja
  full_name: Barkhofen, Sonja
  id: '48188'
  last_name: Barkhofen
citation:
  ama: Schütte P, Weich T, Barkhofen S. Meromorphic Continuation of Weighted Zeta
    Functions on Open Hyperbolic Systems. <i>Communications in Mathematical Physics</i>.
    2023;398:655-678. doi:<a href="https://doi.org/10.1007/s00220-022-04538-z">https://doi.org/10.1007/s00220-022-04538-z</a>
  apa: Schütte, P., Weich, T., &#38; Barkhofen, S. (2023). Meromorphic Continuation
    of Weighted Zeta Functions on Open Hyperbolic Systems. <i>Communications in Mathematical
    Physics</i>, <i>398</i>, 655–678. <a href="https://doi.org/10.1007/s00220-022-04538-z">https://doi.org/10.1007/s00220-022-04538-z</a>
  bibtex: '@article{Schütte_Weich_Barkhofen_2023, title={Meromorphic Continuation
    of Weighted Zeta Functions on Open Hyperbolic Systems}, volume={398}, DOI={<a
    href="https://doi.org/10.1007/s00220-022-04538-z">https://doi.org/10.1007/s00220-022-04538-z</a>},
    journal={Communications in Mathematical Physics}, author={Schütte, Philipp and
    Weich, Tobias and Barkhofen, Sonja}, year={2023}, pages={655–678} }'
  chicago: 'Schütte, Philipp, Tobias Weich, and Sonja Barkhofen. “Meromorphic Continuation
    of Weighted Zeta Functions on Open Hyperbolic Systems.” <i>Communications in Mathematical
    Physics</i> 398 (2023): 655–78. <a href="https://doi.org/10.1007/s00220-022-04538-z">https://doi.org/10.1007/s00220-022-04538-z</a>.'
  ieee: 'P. Schütte, T. Weich, and S. Barkhofen, “Meromorphic Continuation of Weighted
    Zeta Functions on Open Hyperbolic Systems,” <i>Communications in Mathematical
    Physics</i>, vol. 398, pp. 655–678, 2023, doi: <a href="https://doi.org/10.1007/s00220-022-04538-z">https://doi.org/10.1007/s00220-022-04538-z</a>.'
  mla: Schütte, Philipp, et al. “Meromorphic Continuation of Weighted Zeta Functions
    on Open Hyperbolic Systems.” <i>Communications in Mathematical Physics</i>, vol.
    398, 2023, pp. 655–78, doi:<a href="https://doi.org/10.1007/s00220-022-04538-z">https://doi.org/10.1007/s00220-022-04538-z</a>.
  short: P. Schütte, T. Weich, S. Barkhofen, Communications in Mathematical Physics
    398 (2023) 655–678.
date_created: 2022-05-04T12:27:46Z
date_updated: 2026-02-18T10:41:07Z
department:
- _id: '10'
- _id: '548'
- _id: '623'
- _id: '15'
doi: https://doi.org/10.1007/s00220-022-04538-z
external_id:
  arxiv:
  - '2112.05791'
intvolume: '       398'
language:
- iso: eng
page: 655-678
publication: Communications in Mathematical Physics
status: public
title: Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems
type: journal_article
user_id: '49178'
volume: 398
year: '2023'
...