数论中二元二次型理论的起源和早期发展  

The Origin and Early Development of Binary Quadratic Forms in Number Theory

作　　者：胡俊美 贾随军[2] HU Junmei;JIA Suijun(Department of Mathematics and Physics,Shijiazhuang Tiedao University,Shijiazhuang 050043,Hebei,China;Educational Institute,Zhejiang International Studies University,Hangzhou 310012,Zhejiang,China.)

机构地区：[1]石家庄铁道大学数理系,河北石家庄050043 [2]浙江外国语学院教育科学学院,浙江杭州310012

出　　处：《咸阳师范学院学报》2018年第4期14-19,共6页Journal of Xianyang Normal University

基　　金：国家自然科学基金项目(11501379;11461059)

摘　　要：二元二次型理论是数论的一个重要分支,且与初等数论中许多最优美的定理有关。通过研究原始文献,系统分析了二元二次型从最初萌芽到形成独立完整的研究对象的历史过程,揭示了数学中化特殊为一般、变具体为抽象、从个别对象到分类研究方法的重要意义,对其他数学学科的发展产生了一定影响。The theory of binary quadratic forms, one of the important branches in number theory,is related to many of the most beautiful theorems in elementary number theory. On the basis of the detailed study on the original literature, this paper analyzed the evolution of binary quadratic forms from the emergence to the development as an independent object. It revealed the important significance of the methodology from particularity to generalization, from specification to abstraction and from individual objects to taxonomic approach. At the same time, the theory of binary quadratic forms has exerted a measure of influence on the development of other branches in mathematics.

关 键 词：二元二次型 型的等价 型的合成 代数数论 

分 类 号：N09[自然科学总论—科学技术哲学] O11[理学—数学]