---
_id: '67136'
abstract:
- lang: eng
  text: A weighted dynamical version $\mathbf{Z}_f$ of the classical Ihara zeta function
    is presented on connected finite regular graphs, expressed in terms of weighted
    periodic orbit data. We establish its meromorphic continuation, with poles given
    by the resonances of the associated non-backtracking transfer operator acting
    on a suitable Banach space, and compute its residues. At simple spectral parameters,
    the residue of $\mathbf{Z}_f$ is identified with the invariant Ruelle distribution
    on the graph phase space. Combining this result with a relation obtained by Arends-Palmirotta,
    we further derive Patterson-Sullivan and Wigner residue formulae. This provides
    a finite-graph analogue of residue formulae for weighted dynamical zeta functions
    for geodesic flow on rank one locally symmetric spaces, in the spirit of Schütte-Barkhofen-Weich.
author:
- first_name: Guendalina
  full_name: Palmirotta, Guendalina
  id: '109467'
  last_name: Palmirotta
citation:
  ama: Palmirotta G. Residues of weighted dynamical Ihara zeta functions on finite
    regular graphs. Published online 2026.
  apa: Palmirotta, G. (2026). <i>Residues of weighted dynamical Ihara zeta functions
    on finite regular graphs</i>.
  bibtex: '@article{Palmirotta_2026, title={Residues of weighted dynamical Ihara zeta
    functions on finite regular graphs}, author={Palmirotta, Guendalina}, year={2026}
    }'
  chicago: Palmirotta, Guendalina. “Residues of Weighted Dynamical Ihara Zeta Functions
    on Finite Regular Graphs,” 2026.
  ieee: G. Palmirotta, “Residues of weighted dynamical Ihara zeta functions on finite
    regular graphs.” 2026.
  mla: Palmirotta, Guendalina. <i>Residues of Weighted Dynamical Ihara Zeta Functions
    on Finite Regular Graphs</i>. 2026.
  short: G. Palmirotta, (2026).
date_created: 2026-09-14T07:49:06Z
date_updated: 2026-09-14T07:51:03Z
department:
- _id: '548'
- _id: '10'
- _id: '34'
language:
- iso: eng
page: '53'
status: public
title: Residues of weighted dynamical Ihara zeta functions on finite regular graphs
type: preprint
user_id: '109467'
year: '2026'
...