报告题目：Truncated Hecke Type Identities and Inequalities for the Overpartition Function
报告人：张文静，湖南大学
报告时间：11月26日16:00-18:00
地点：数理楼135教室
报告摘要：Motivated by the work of Wang and Yee, we obtain two extensions of truncated versions of Jacobi's triple product series.
As a consequence, we derive several inequalities for the partition function $t(n)$ counting the partition triples
$(\lambda, \mu,\nu)$ of $n$ such that the total sum of parts of $\lambda$, $\mu$ and $\nu$ is $n$.
We also reprove the conjecture made by Guo-Zeng.
Moreover, we give some the extensions of truncated theorems obtained by Andrews, Merca, Wang and Yee.
Our proofs heavily rely on the theory of Bailey pairs.
In this talk, we will also introduce some inequalities for the overpartition function.
Let $\overline{p}(n)$ denote the overpartition funtion.
Engel showed that for $n\geq2$, $\overline{p}(n)$ satisfied the Tur\'{a}n inequalities,
that is, $\overline{p}(n)^2-\overline{p}(n-1)\overline{p}(n+1)>0$ for $n\geq2$.
In this talk, we prove several inequalities for $\overline{p}(n)$.
Moreover, motivated by the work of Chen, Jia and Wang,
we find that the higher order Tur\'{a}n inequalities of $\overline{p}(n)$ can also be determined.
报告人简介：张文静，湖南大学数学学院助理教授，2019年博士毕业于天津大学。研究的主要兴趣是组合数学，尤其是整数分拆，q-级数，仿theta函数以及模形式。