报告题目 (Title)：Sums of four polygonal numbers: precise formulas（四个多边形数之和：确切公式）
报告人 (Speaker)：王好武 教授（武汉大学）
报告时间 (Time)：2024年9月14日(周六) 18:30
报告地点 (Place)：#腾讯会议：827-813-644（会议密码：666666）
邀请人(Inviter)：孙孟锋
主办部门：理学院数学系
报告摘要：In this talk we give unified formulas for the numbers of representations of positive integers as sums of four generalized m-gonal numbers, and as restricted sums of four squares under a linear condition, respectively. The formulas are given as Z-linear combinations of Hurwitz class numbers. As applications, we prove several Zhi-Wei Sun's conjectures. As by-products, we obtain formulas for expressing the Fourier coefficients of $\vartheta(\tau,z)^4$, $\eta(\tau)^{12}$, $\eta(\tau)^4$ and $\eta(\tau)^8\eta(2\tau)^8$ in terms of the Hurwitz class numbers, respectively. The proof is based on the theory of Jacobi forms.
