Counting modular matrices with specified Euclidean norm
type: Item
instance of: scholarly article
title: Counting modular matrices with specified Euclidean norm
zbMATH Open document ID: 0643.10020
DOI: 10.1016/0097-3165(88)90048-9
author: Morris Newman
published in: Journal of Combinatorial Theory. Series A
publication date: 1988-01-01T00:00:00Z
review text: Let N(x) be the number of matrices \(\left( \begin{matrix} a\\ c\end{matrix} \begin{matrix} b\\ d\end{matrix} \right)\in SL(2,{\mathbb{Z}})\) whose Euclidean norm \(a^ 2+b^ 2+c^ 2+d^ 2\) does not exceed x. Then \(\lim_{x\to \infty}N(x)/x=6\).
Mathematics Subject Classification ID: 11F06
Mathematics Subject Classification ID: 11N45
Mathematics Subject Classification ID: 20H05
zbMATH DE Number: 4047810
zbMATH Keywords: modular group SL(2,\({bbfZ})\)
zbMATH Keywords: sums of squares
zbMATH Keywords: number of matrices
zbMATH Keywords: Euclidean norm
reviewed by: Gerhard Rosenberger
MaRDI profile type: Publication
full work available at URL: 0097-3165(88)90048-9
OpenAlex ID: W1991635118
description: scientific article; zbMATH DE number 4047810