---
res:
  bibo_abstract:
  - 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.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Guendalina
      foaf_name: Palmirotta, Guendalina
      foaf_surname: Palmirotta
      foaf_workInfoHomepage: http://www.librecat.org/personId=109467
  dct_date: 2026^xs_gYear
  dct_language: eng
  dct_title: Residues of weighted dynamical Ihara zeta functions on finite regular
    graphs@
...