报告人：王六权

时 间：2026年10月25日 16:00

地 点：L-2620

报告摘要：Kanade and Russell conjectured seventeen Rogers--Ramanujan type identities of modulus 12. Eleven of these identities involving triple sums were proved by Bringmann--Jennings-Shaffer--Mahlburg and by Rosengren. Motivated by these works and using similar methods, we settle all the six remaining conjectures including two triple sum identities labeled I5a and I6a originated from Russell's thesis and four quadruple sum identities labeled 7, 7a, 8 and 8a. Our proof of the triple sum identities combines linear recurrences, q-difference equations, and q-series summation formulas. For the quadruple sum identities, we represent the sums as contour integrals whose integrands are infinite products and evaluate them by residue calculus. The resulting residues reduce to single sum cubic basic hypergeometric series, and we are able to express them as infinite products.

专家简介：王六权，武汉大学数学与统计学院教授，主要从事组合数学与数论领域的研究，研究课题多集中在 q-级数、整数分拆、特殊函数、模形式理论等方面。迄今在 Adv. in Math., Trans.Amer. Math. Soc., J. Combin. Theory Ser. A, Adv. in Appl. Math.,J. Number Theory 等期刊上发表学术论文 50 多篇，2021 年入选青年拔尖人才支持计划，先后主持国家自然科学基金青年基金,面上项目, 国家重点研发计划青年科学家项目各一项。