Academic Report of School of Mathematical Sciences [2026] No. 019

(Series Report for High-Level University Construction No. 1278)

Title：The classification and representations of ternary quadratic forms

Speaker：Professor Haigang Zhou (Tongji University)

Time：16:00-17:00, Mar. 27, 2026

Location：Room 2331, Huiwen Building

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 or 8N explicitly. Secondly, we give the weighted sum of representations over each class in every genus of ternary quadratic forms of level 4N or 8N 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. 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.

Speaker Profile：Haigang Zhou  is a professor and doctoral advisor at the School of Mathematical Sciences, Tongji University. His research focuses on number theory and modular forms, with primary interests in Jacobi forms, quadratic forms, and quaternions. His research findings have been published in journals such as the Transactions of the American Mathematical Society and the Mathematische Zeitschriften. He has led several projects funded by the National Natural Science Foundation of China and received the Second Prize in Natural Sciences from the Ministry of Education’s Award for Outstanding Achievements in Scientific Research at Institutions of Higher Education in 2012.

Faculty and students are welcome to attend!

Invited by: Yingnan Wang

School of Mathematical Sciences

March 25, 2026