理学院学术报告——The classification and representations of ternary quadratic form

报告题目： The classification and representations of ternary quadratic forms of level 4N

报告人： 周海港 教授（同济大学）

报告时间：2024年11月15日（周五）下午15: 00-16: 00

报告地点：2B-408

报告摘要：

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, we firstly give the classification of positive definite ternary quadratic forms of level 4N explicitly. Second, we give the weighted sum of representations over each class in every genus of ternary quadratic forms of level 4N 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 of level 4N. 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。解决经典的平方和与线性型联立的丢番图方程组解数问题，给出高阶Jacobi形式空间的维数公式，给出Skew-holomorphic Jacobi形式的迹公式。在Trans. of AMS和Math. Z.等著名期刊发表二十余篇论文，主持多项国家自然科学基金项目，作为主要参与人获教育部2011年度高等学校科学研究优秀成果奖自然科学二等奖。