Conjugacy classes of elliptic elements in the Picard group
type: Item
instance of: scholarly article
zbMATH Open document ID: 0971.20025
publication date: 2001-10-29T00:00:00Z
Mathematics Subject Classification ID: 20H05
Mathematics Subject Classification ID: 20H10
Mathematics Subject Classification ID: 20E45
zbMATH DE Number: 1571096
zbMATH Keywords: Picard group
zbMATH Keywords: non-Fuchsian discrete subgroup of \(\text{PSL}(2,\mathbb{C})\)
zbMATH Keywords: Gaussian integers
zbMATH Keywords: numbers of conjugacy classes of elliptic elements
zbMATH Keywords: quadratic forms
zbMATH Keywords: discriminants
author: Nihal Yilmaz
author: Ismail Naci Cangül
MaRDI profile type: Publication
title: Conjugacy classes of elliptic elements in the Picard group
published in: Turkish Journal of Mathematics
review text: The Picard group \(P\) is a non-Fuchsian discrete subgroup of \(\text{PSL}(2,\mathbb{C})\) having Gaussian integer coefficients. \textit{B. Fine} [Can. J. Math. 28, 481-485 (1976; Zbl 0357.20026)] has shown that the total number of conjugacy classes of elliptic elements is seven.NEWLINENEWLINENEWLINEIn this paper, the authors reduce this number to five. They use quadratic forms \(az\overline z+bz+\overline b\overline z+c\) with \(a,c\in\mathbb{Z}\) and \(b\in\mathbb{Z}(i)\). If \(b=b_1+ib_2\), then the discriminant of this form is defined to be \(D=b^2_1+b^2_2-ac\).NEWLINENEWLINENEWLINEClassification is then made according to the discriminant of these forms modulo 4.
reviewed by: Turgut Başkan
description: scientific article