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.