Zeta Function at Zero for Surfaces with Boundary

2018/03/29 by Charles Hadfield, Hadfield, Charles · 1 citation
Mathematics · #37C30 #37D40 #58J50 #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #math.DS #msc:37C30 #msc:37D40 #msc:58J50

paper · pdf · doi:10.48550/arxiv.1803.10982

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

openalex publication_date 2018/03/29 · arxiv created 2018/07/25 · arxiv updated 2018/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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