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

TL;DR

This paper introduces a unified method to derive and prove 2- and 3-dissections of second, sixth, and eighth-order mock theta functions using Appell--Lerch sum transformations and symbolic computation.

Contribution

It develops a systematic approach leveraging Appell--Lerch sum transformations and Maple computations to obtain explicit dissection identities for specific mock theta functions.

Findings

Explicit 2- and 3-dissections of certain mock theta functions are derived.

The method simplifies proving dissection identities using symbolic computation.

A unified framework for dissecting higher-order mock theta functions is established.

Abstract

In this paper, we develop a unified method for obtaining and proving $m$-dissections of mock theta functions. Our approach builds upon a transformation formula for Appell--Lerch sums due to Hickerson and Mortenson, which allows these sums to be expressed as linear combinations of Appell--Lerch sums together with suitable theta products. By systematically exploiting this representation, and through extensive symbolic computations carried out in Maple, we derive explicit dissection identities in a direct and effective manner. We focus exclusively on the cases of $2$- and $3$-dissections.