Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Zeta Function at Zero for Surfaces with Boundary   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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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin