题目：           Partitions related to mock theta functions

报告人：     王六权 (武汉大学)

时间地点：   2018.04.19  14:00pm  N205

摘要：           Let $\omega(q)$ be the third order mock theta function due to Ramanujan and Watson. In his 2007 paper in Invent. Math., Andrews interpreted the coefficients of $\omega(q)$ as a partition function $p_{\omega}(n)$. He also introduced the concepts of odd rank and k-marked odd Durfee symbols for this kind of partitions. In this talk, we will present some new congruences satisfied by $p_{\omega}(n)$ and the smallest parts function associated to it. Meanwhile, we will discuss the arithmetic properties of odd ranks and k-marked odd Durfee symbols. Applying the properties we find, we give proofs to Andrews’ conjectures on the parity of k-marked odd Durfee symbols.