数学学科Seminar第2741讲 4N级三元二次型的分类与表示

创建时间:  2024/10/10  龚惠英   浏览次数:   返回

报告题目 (Title):4N级三元二次型的分类与表示(The classification and representations of ternary quadratic forms of level 4N)

报告人 (Speaker):周海港 教授(同济大学)

报告时间 (Time):2024年10月11日(周五) 10:30-11:30

报告地点:校本部E408

邀请人(Inviter):王晓霞

主办部门:金沙威尼斯欢乐娱人城数学系

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 $N$, 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.

上一条:数学学科Seminar第2742讲 追求更满意算法,打造新一代软件

下一条:数学学科Seminar第2740讲 关于Hermite多项式与Hermite级数


数学学科Seminar第2741讲 4N级三元二次型的分类与表示

创建时间:  2024/10/10  龚惠英   浏览次数:   返回

报告题目 (Title):4N级三元二次型的分类与表示(The classification and representations of ternary quadratic forms of level 4N)

报告人 (Speaker):周海港 教授(同济大学)

报告时间 (Time):2024年10月11日(周五) 10:30-11:30

报告地点:校本部E408

邀请人(Inviter):王晓霞

主办部门:金沙威尼斯欢乐娱人城数学系

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 $N$, 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.

上一条:数学学科Seminar第2742讲 追求更满意算法,打造新一代软件

下一条:数学学科Seminar第2740讲 关于Hermite多项式与Hermite级数