论文标题
晶格和数字的几何形状
Lattices and the Geometry of Numbers
论文作者
论文摘要
在本文中，我们讨论了晶格的特性及其在理论和算法数理论中的应用。 Minkowski关于晶格的结果启动了数字的几何学主题，该主题使用几何来研究代数数的特性。它在数学的其他各个领域中都有应用，特别是对二芬太汀方程的研究，功能分析的分析等。本文将回顾数量几何领域中发生的所有主要发展。在本文中，我们将首先概述晶格的概念，然后讨论其具有的几何特性及其应用。
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.
