Lattices and the Geometry of Numbers

In this paper we discuss about properties of lattices and its application in theoretical and algorithmic number theory. This result of Minkowski regarding the lattices initiated the subject of Geometry of Numbers, which uses geometry to study the properties of algebraic numbers. It has application o...

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Bibliographic Details
Published in:arXiv.org 2021-01
Main Author: Ghosh, Sourangshu
Format: Article
Language:English
Subjects:
Euclidean geometry
Existence theorems
Geometry
Number theory
Symmetrical bodies
Online Access:Get full text
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Summary:In this paper we discuss about properties of lattices and its application in theoretical and algorithmic number theory. This result of Minkowski regarding the lattices initiated the subject of Geometry of Numbers, which uses geometry to study the properties of algebraic numbers. It has application on various other fields of mathematics especially the study of Diophantine equations, analysis of functional analysis etc. This paper will review all the major developments that have occurred in the field of geometry of numbers. In this paper we shall first give a broad overview of the concept of lattice and then discuss about the geometrical properties it has and its applications.
ISSN:2331-8422
DOI:10.48550/arxiv.2010.00245