报告题目 (Title):关于广义秩为3的Nahm和的Mizuno猜想
报告人 (Speaker):王博学(武汉大学)
报告时间(Time):2025年6月8日(周日) 10:30
报告地点 (Place):GJ303
邀请人(Inviter):陈旦旦
主办部门:理学院数学系
报告摘要:Mizuno providied 15 examples of generalized rank three Nahm sums with symmetrizer $\mathrm{diag}(1,2,2)$ which are conjecturally modular. Using the theory of Bailey pairs and some $q$-series techniques, we establish a number of triple sum Rogers--Ramanujan type identities. These identities confirm the modularity of all of Mizuno's examples except for two non-modular cases. We show that the two exceptional cases of Nahm sums are sums of modular forms of weights $0$ and $1$. We also prove Mizuno’s conjectural modular transformation formulas for two vector-valued functions consisting of Nahm sums with symmetrizers $\mathrm{diag}(1,1,2)$ and $\mathrm{diag}(1,2,2)$.