Short proofs of Ramanujan-like identities for the eighth order mock theta function $V_{0}(q)$

TL;DR

This paper provides concise proofs of Ramanujan-like identities for the eighth order mock theta function V_0(q) using Appell functions, and extends these identities in the context of ranks and Maass forms.

Contribution

It introduces short proofs of known identities and generalizes them in the framework of ranks and Maass forms, building on prior work by Chan, Mao, and others.

Findings

Short proofs of Ramanujan-like identities for V_0(q)

Generalization of identities related to ranks and Maass forms

Connections to Dyson's ranks and modular objects

Abstract

Using Appell function properties we give short proofs of Ramanujan-like identities for the eighth order mock theta function $V_0(q)$ after work of Chan and Mao; Mao; and Brietzke, da Silva, and Sellars. We also present a generalization of the identities in the spirit of celebrated results of Bringmann, Ono, and Rhoades on Dyson's ranks and Maass forms.