English

Zeta Function at Zero for Surfaces with Boundary

Dynamical Systems 2018-07-26 v2

Abstract

We study the Ruelle zeta function at zero for negatively curved oriented surfaces with boundary. At zero, the zeta function has a zero and its multiplicity is shown to be determined by the Euler characteristic of the surface. This is shown by considering certain Ruelle resonances and identifying their multiplicity with dimensions of the relative cohomology of the surface.

Keywords

Cite

@article{arxiv.1803.10982,
  title  = {Zeta Function at Zero for Surfaces with Boundary},
  author = {Charles Hadfield},
  journal= {arXiv preprint arXiv:1803.10982},
  year   = {2018}
}

Comments

17 pages, clarification of map defined in Section 4, minor change in proof of injectivity

R2 v1 2026-06-23T01:08:37.289Z