## Thursday, March 4, 2021

### Liuquan Wang (Wuhan University) March 4, 2021 - 3:55 PM (IST)

The next talk is by Liuquan Wang of Wuhan University.

Talk announcement

Title: Parity of coefficients of mock theta functions

Speaker: Liuquan Wang (Wuhan University, PRC)

When: March 4, 2021 - 3:55 PM - 5:00 PM (IST)

Where: Zoom:  Please write to sfandnt@gmail.com for a link or watch here:

Abstract: We study the parity of coefficients of classical mock theta functions. Suppose $g$ is a formal power series with integer coefficients, and let $c(g;n)$ be the coefficient of $q^n$ in its series expansion. We say that $g$ is of parity type $(a,1-a)$ if $c(g;n)$ takes even values with probability $a$ for $n\geq 0$. We show that among the 44 classical mock theta functions, 21 of them are of parity type $(1,0)$. We further conjecture that 19 mock theta functions are of parity type $(\frac{1}{2},\frac{1}{2})$ and 4 functions are of parity 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 parity type $(1,0)$.