Completions and algebraic formulas for the coefficients of Ramanujan's mock theta functions

TL;DR

This paper extends Ramanujan's mock theta functions to harmonic weak Maass forms of weight 1/2 and derives algebraic formulas for their coefficients using advanced mathematical techniques.

Contribution

It introduces new harmonic weak Maass forms related to mock theta functions and provides algebraic formulas for their coefficients via the Millson theta lift.

Findings

Constructed harmonic weak Maass forms with mock theta functions as holomorphic parts

Derived finite algebraic formulas for mock theta coefficients

Connected coefficients to traces of singular moduli

Abstract

We present completions of mock theta functions to harmonic weak Maass forms of weight $1/2$ and algebraic formulas for the coefficients of mock theta functions. We give several harmonic weak Maass forms of weight $1/2$ that have mock theta functions as their holomorphic part. Using these harmonic weak Maass forms and the Millson theta lift we compute finite algebraic formulas for the coefficients of the appearing mock theta functions in terms of traces of singular moduli.