学术报告会: The classification and representations of ternary quadratic forms

报告题目：The classification and representations of ternary quadratic forms

报 告 人： 周海港      (同济大学     教授)

报告时间：2026年7月8日周三10:30

报告地点：S3-313

Abstract：Classifications and representations are two main topics in the theory of quadratic forms. In this talk, we consider these topics of ternary quadratic forms. For a given squarefree integer N, firstly we give the classification of positive definite ternary quadratic forms of level 4N  or  8N explicitly. Secondly, we give the weighted sum of representations over each class in every genus of ternary quadratic forms of level 4N or  8N by using quaternion algebras and Jacobi forms. The formulas are involved with modified Hurwitz class number. As a corollary, we get  a formula for the class number of ternary quadratic forms. As applications, we give an explicit base of Eisenstein series space of modular forms of weight 3/2 of level 4N, and give new proofs of some interesting identities involving representation number of ternary quadratic forms.

个人简介：

周海港，同济大学数学科学学院教授, 博士生导师。从事数论与模形式研究，主要研究兴趣在 Jacobi 形式、二次型和四元代数等方面，研究成果发表在 Math. Comp., Trans. of  AMS 和 Math. Z.等期刊上，主持多项国家自然科学基金项目，2012年获教育部高等学校科学研究优秀成果奖自然科学二等奖。