星光直播 星光直播 报告[2026]019号

(高水平大学建设系列报告1278号)

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

报告人：周海港 教授 （同济大学）

报告时间：2026年3月27日16:00-17:00

报告地点：汇文楼办公区2331

报告内容：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.

报告人简历： 周海港，同济大学星光直播 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。

欢迎师生参加！

邀请人：王英男

星光直播

2026年3月25日