»ã±¨±êÌâ (Title)£º4N¼¶ÈýÔª¶þ´ÎÐ͵ķÖÀàÓ밵ʾ£¨The classification and representations of ternary quadratic forms of level 4N£©

»ã±¨ÈË (Speaker)£ºÖܺ£¸Û ½ÌÊÚ£¨Í¬¼Ã´óѧ£©

»ã±¨¹¦·ò (Time)£º2024Äê10ÔÂ11ÈÕ(ÖÜÎå) 10:30-11:30

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»ã±¨ÌáÒª£ºClassifications 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.