报告题目 (Title)：Rogers-Ramanujan型等式与Nahm和 （Rogers-Ramanujan type identities and Nahm sums）
报告人 (Speaker)：王六权 教授（武汉大学）
报告时间 (Time)：2024年7月2日(周二) 10:00—12:00
报告地点：校本部GJ303
邀请人(Inviter)：王晓霞、陈旦旦
报告摘要：Let $r\geq 1$ be a positive integer, $A$ a real positive definite symmetric $r\times r$ matrix, $B$ a vector of length $r$, and $C$ a scalar. Nahm's problem is to describe all such $A,B$ and $C$ with rational entries for which $$F_{A,B,C}(q)=\sum_{n=(n_1,\dots,n_r)\in (\mathbb{Z}_{r\geq 0})^r}\frac{q^{\frac{1}{2}n^\mathrm{T}An+n^\mathrm{T}B+C}} {(q)_{n_1}\cdots (q)_{n_r}}$$ is a modular form. Zagier completely solved the rank one case. When the rank r=2,3, Zagier presented many examples of $(A,B,C)$ for which $F_{A,B,C}(q)$ appears to be a modular form. We present a number of Rogers-Ramanujan type identities involving double and triple sums, which give modular form representations for Zagier’s rank two and rank three examples. We will also discuss the modularity of some other generalized Nahm sums.