汇报标题 (Title)：4N级三元二次型的分类与暗示（The classification and representations of ternary quadratic forms of level 4N）
汇报人 (Speaker)：周海港 教授（同济大学）
汇报功夫 (Time)：2024年10月11日(周五) 10:30-11:30
汇报地址：校本部E408
约请人(Inviter)：王晓霞
主办部门：理学院数学系
汇报提要：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 $N$, firstly we give the classification of positive definite ternary quadratic forms of level $4N$ explicitly. Secondly, 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.
