报告人：王六权（武汉大学）

邀请人：胡怡宁

报告题目：Parity of coefficients of mock theta functions

报告时间：2020年10月8日9：00-11：00

报告地点：腾讯会议ID：321 505 633

报告摘要：We study the parity of coefficients of classical mock theta functions. Let $c(g;n)$ be the coefficient of $q^n$ in the series expansion of $g(q)$. For a power series $g(q)$ with integer coefficients, we say that $g$ is of type $(a,1-a)$ modulo 2 if $c(g;n)$ takes even values with probability $a$. We show that among the 44 classical mock theta functions, 21 of them are of type $(1,0)$ modulo 2. We further conjecture that 19 mock theta functions are of type $(\frac{1}{2},\frac{1}{2})$ and 4 functions are of type $(\frac{3}{4},\frac{1}{4})$. We also give characterizations of $n$ such that $c(g;n)$ is odd for the mock theta functions of type $(1,0)$.

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》、《Advances in Applied Mathematics》、《Journal of Number Theory》、《Ramanujan Journal》等期刊上发表学术论文30多篇。