報告題目： The classification and representations of ternary quadratic forms of level 4N

報告人： 周海港 教授（同濟大學）

報告時間：2024年11月15日（周五）下午15: 00-16: 00

報告地點：2B-408

報告摘要：

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.

報告人簡介：

周海港，同濟大學數學科學學院教授, 博士生導師。從事數論與模形式研究，主要研究興趣在Jacobi形式、二次型和四元代數等方面。解決經典的平方和與線性型聯立的丟番圖方程組解數問題，給出高階Jacobi形式空間的維數公式，給出Skew-holomorphic Jacobi形式的跡公式。在Trans. of AMS和Math. Z.等著名期刊發表二十余篇論文，主持多項國家自然科學基金項目，作為主要參與人獲教育部2011年度高等學校科學研究優秀成果獎自然科學二等獎。