Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A dynamical systems analogue of Lichtenbaum's conjectures on special
  values of Hasse-Weil zeta functions   In recent years Lichtenbaum has conjectured a description for the special
values of Hasse--Weil zeta functions in terms of ``Weil-\'etale cohomology''.
In earlier papers we studied a class of foliated dynamical systems which had
some similarities with arithmetic schemes. Assuming that certain zeta
regularized determinants exist we now prove an analogue of Lichtenbaum's
conjectures for a particularly simple class of such dynamical systems: Using
results of \'Alvarez L\'opez and Kordyukov we express the leading coefficient
$\zeta^*_R (0)$ of the Ruelle zeta function $\zeta_R (s)$ at $s = 0$ in terms
of analytic torsion. We then apply the Cheeger--M\"uller theorem to replace the
analytic torsion by the Reidemeister torsion with respect to harmonic bases.
For our dynamical systems the latter can be expressed by the same recipe as the
one in Lichtenbaum's conjectures.

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The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: econ