汇报标题 (Title)：关于广义秩为3的Nahm和的Mizuno猜测
汇报人 (Speaker)：王博学（武汉大学）
汇报功夫（Time）：2025.6.8（周日）10：30
汇报地址 (Place)：校本部GJ303
约请人(Inviter)：陈旦旦
主办部门：理学院数学系
汇报提要：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 $\mathrm{diag}(1,2,2)$.
