Remarks on the Patterson–Selberg zeta function, black hole vacua and extremal CFT partition functions

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.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker's 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’.

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