Mock theta functions and characters of N=3 superconformal modules II

Abstract

We obtain an explicit formula for the mock theta function ${\Phi }^{[m,s]}$ in the case when either $m$ or $s$ is a half of an odd integer by using the coroot lattice of $D(2,1;a)$. This enables us, together with the recurrence formula for ${\Phi }^{[m,s]}$, to know ${\Phi }^{[m,s]}$ for all $m$ and $s$. As its application, we deduce explicit formulas for the character and the supercharacter of N=3 modules obtained from the quantum Hamiltonian reduction of $\widehat{osp}(3|2)$-modules.