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Remarks on the Patterson-Selberg zeta function, black hole vacua and extremal CFT partition functions. (English) Zbl 1251.83037

Summary: We consider some applications (old and new) of the Patterson-Selberg zeta function to 3D gravity with a negative cosmological constant. We also consider 2D black hole vacua with a parabolic generator of their holonomy.

MSC:

83C57 Black holes
11M36 Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas)
30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization)
35B34 Resonance in context of PDEs
81T20 Quantum field theory on curved space or space-time backgrounds
83C80 Analogues of general relativity in lower dimensions
53C29 Issues of holonomy in differential geometry
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