| Abstract: |
| 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. |
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