Lattices and the Geometry of Numbers
Sourangshu Ghosh *
Department of Civil Engineering, Indian Institute of Technology Kharagpur, West Bengal, India.
*Author to whom correspondence should be addressed.
Abstract
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 gives an elementary introduction to 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.
Keywords: Lattices, geometry of numbers, minkowski theorem