Further q-reflections on the modulo 9 Kanade-Russell (conjectural) identities

TL;DR

This paper explores conjectured identities related to modulo 9 Kanade-Russell identities, expanding the understanding of these mathematical structures and proposing new conjectures in the area.

Contribution

It analyzes four Hickerson conjectured identities, complements existing identities, and introduces new identities and conjectures in the field.

Findings

Identification of four Hickerson conjectured identities

Development of a profile of new identities and conjectures

Extension of the modulo 9 Kanade-Russell identities

Abstract

We examine four identities conjectured by Hickerson which complement five modulo $9$ Kanade--Russell identities, and we build up a profile of new identities and new conjectures not unlike those found by Uncu and Zudilin.