The number of solutions of bounded height to a system of linear equations
type: Item
instance of: scholarly article
title: The number of solutions of bounded height to a system of linear equations
zbMATH Open document ID: 0773.11022
author: Jeffrey Lin Thunder
published in: Journal of Number Theory
publication date: 1993-05-16T00:00:00Z
full work available at URL: http://hdl.handle.net/2027.42/30992
review text: The author considers the number of solutions with height \(\leq B\) of systems of homogeneous or inhomogeneous linear equations over a number field. Explicit asymptotic estimates with error terms are given for the number of such solutions as \(B\to\infty\). The constants involved in the formulas depend on the parameters of the number field. Similar results are obtained for the number of lattice points in certain bounded domains.
Mathematics Subject Classification ID: 11D04
Mathematics Subject Classification ID: 11J99
zbMATH DE Number: 166072
zbMATH Keywords: bounded height
zbMATH Keywords: system of linear diophantine equations
zbMATH Keywords: explicit asymptotic estimates with error terms
zbMATH Keywords: number of solutions
zbMATH Keywords: number of lattice points
zbMATH Keywords: bounded domains
reviewed by: István Gaál
MaRDI profile type: Publication
OpenAlex ID: W1978971318
DOI: 10.1006/JNTH.1993.1021
description: scientific article; zbMATH DE number 166072