报告人：洪楠坤博士研究生（南洋理工大学数理学院）
报告时间：2019年10月14日，9:00-10：00
报告地点：精正楼301
报告摘要：Ramanujan had three famous congruences for the partition function modulo 5, 7 and 11. F. J. Dyson defined the the rank of partitions and conjectured that ranks could provide combinatorial explanations for the 5 and 7 cases. A. O. L. Atkin and H. P. F. Swinnerton-Dyer proved his conjecture using generating functions for the rank difference modulo 5 and 7.
Ramanujan recorded several entries which are related to generating functions of the rank modulo different integers. In this talk, we will show how to get 3-dissection of ranks modulo 9 and give an identity involving generating functions of ranks modulo 3 and 9. By utilizing Ramanujan's entries, we can get some new identities. Part of the result is joint work with Song Heng Chan, Jerry and Jeremy Lovejoy.