2- and 3-Dissections of Second-, Sixth-, and Eighth-Order Mock Theta Functions

Abstract

In this paper, we develop a systematic method for obtaining and proving $m$-dissections of mock theta functions. In 2014, Hickerson and Mortenson showed how to derive and prove identities for Ramanujan's mock theta functions and Hecke-type indefinite theta series using Appell--Lerch sums. We build on their transformation formula method, combining it with symbolic computations and algorithms for the theory of modular functions. We focus exclusively on the cases of 2- and 3-dissections.

1. We have reorganised the paper. 2. We have found the complete $3$-dissections of the second-order mock theta function $\hat{I}{¼}_2$ and the eighth-order mock theta function $V_{0,8}$