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:金沙威尼斯欢乐娱人城数学系
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.