The Schottky-Klein prime function and counting functions for Fenchel double crosses
type: Item
instance of: scholarly article
title: The Schottky-Klein prime function and counting functions for Fenchel double crosses
zbMATH Open document ID: 1469.30094
author: Mark Pollicott
published in: Monatshefte für Mathematik
publication date: 2021-06-08T00:00:00Z
review text: The author establishes a relation between problems of convergence of the classical Schottky-Klein prime function in complex analysis and a counting problem for pairs of geodesics in hyperbolic geometry studied by Fenchel. He associates to the counting problem an analytic function analogous to the Poincaré series and he solves the counting problem using ideas from ergodic theory and thermodynamic formalism.
Mathematics Subject Classification ID: 30F40
Mathematics Subject Classification ID: 37D35
Mathematics Subject Classification ID: 37D40
Mathematics Subject Classification ID: 30E99
zbMATH DE Number: 7356431
zbMATH Keywords: Schottky-Klein function
zbMATH Keywords: Schottky groups
zbMATH Keywords: orbital counting function
reviewed by: Athanase Papadopoulos
MaRDI profile type: Publication
full work available at URL: s00605-021-01547-3
OpenAlex ID: W3156701083
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DOI: 10.1007/S00605-021-01547-3
description: scientific article; zbMATH DE number 7356431