题目: Sums of four polygonal numbers: precise formulas 

报告人：王好武，武汉大学

时间：5月26日（星期日）10:30

地点：五教5106

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.