报告题目：Generating functions and congruences for k-colored generalized Frobenius partitions

报告人：王六权副教授

报告时间：2021/06/21 09:30-11:00

报告地点：腾讯会议613 832 785

报告摘要：Let $k$ and $n$ be positive integers. Let $c\phi_{k}(n)$ denote the number of $k$-colored generalized Frobenius partitions of $n$, and let $\mathrm{C}\Phi_k(q)$ be its generating function. In this talk, we present a new method for finding representations of $\mathrm{C}\Phi_k(q)$ using the theory of modular forms. In particular, using this method, we found alternative representations for $\mathrm{C}\Phi_k(q)$ for all $k\leq 17$. We also discuss some relations between $c\phi_k(n)$ and the ordinary partition function $p(n)$. Meanwhile, we will present some interesting congruences satisfied by $c\phi_k(n)$. This talk is mainly based on a joint work with Heng Huat Chan and Yifan Yang

报告人简介：王六权，2017年博士毕业于新加坡国立大学数学系，现为武汉大学副教授。他主要从事数论、组合分析、q级数及特殊函数理论的研究，迄今在《Advances in Mathematics》,《Transactions of the American Mathematical Society》、《Journal of Number Theory》、《Acta Arithmetica》、《Ramanujan Journal》等著名期刊上发表学术论文30多篇，目前正主持国家自然科学基金青年项目一项。