preprint
Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems
Philipp
Schütte
author 50168
Tobias
Weich
author 491780000-0002-9648-6919
Sonja
Barkhofen
author 48188
10
department
548
department
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.
2021
eng
2112.05791
Schütte, Philipp, Tobias Weich, and Sonja Barkhofen. “Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems,” 2021.
Schütte, P., Weich, T., & Barkhofen, S. (2021). <i>Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems</i>.
@article{Schütte_Weich_Barkhofen_2021, title={Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems}, author={Schütte, Philipp and Weich, Tobias and Barkhofen, Sonja}, year={2021} }
P. Schütte, T. Weich, S. Barkhofen, (2021).
Schütte, Philipp, et al. <i>Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems</i>. 2021.
Schütte P, Weich T, Barkhofen S. Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems. Published online 2021.
P. Schütte, T. Weich, and S. Barkhofen, “Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems.” 2021.
310592022-05-04T12:27:46Z2022-05-17T12:03:53Z