Estimates for the number of automorphisms of a Riemann surface
type: Item
instance of: scholarly article
title: Estimates for the number of automorphisms of a Riemann surface
zbMATH Open document ID: 0880.30034
published in: Siberian Mathematical Journal
publication date: 1998-01-05T00:00:00Z
review text: The Hurwitz formula, \[ N \leq 84(g-1), \] estimates the maximal number \(N\) of automorphisms of a Riemann surface of genus \(g>1\). This estimate is sharp, and the equality is realized only for arithmetic Riemann surfaces (i.e. Riemann surfaces uniformized by arithmetic Fuchsian groups). The author improves the estimate for the case of non-arithmetic Riemann surfaces: \[ N \leq 157(g-1)/7. \] He shows that this estimate is sharp. It is attained for infinitely many mutually non-homeomorphic Riemann surfaces. Among them, the surface of genus 50 is the one of minimum genus.
Mathematics Subject Classification ID: 30F10
Mathematics Subject Classification ID: 57M60
zbMATH DE Number: 1099583
zbMATH Keywords: Riemann surface
zbMATH Keywords: group of automorphisms
zbMATH Keywords: Hurwitz estimate
zbMATH Keywords: arithmetic and non-arithmetic Riemann surfaces
author: Mikhail Belolipetsky
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1099583