# Rank two false theta functions and Jacobi forms of negative definite matrix index

## TL;DR

This paper explores rank two false theta functions linked to the A2 root lattice, demonstrating their role as Fourier coefficients of a specific Jacobi form and deriving related hypergeometric q-series identities.

## Contribution

It establishes a connection between rank two false theta functions and Jacobi forms of negative definite matrix index, providing new hypergeometric q-series identities.

## Key findings

- False theta functions are Fourier coefficients of a meromorphic Jacobi form.
- Derived new hypergeometric q-series identities.
- Linked rank two false theta functions to the A2 root lattice.

## Abstract

In this paper, we study a family of rank two false theta series associated to the root lattice of type $A_2$. We show that these functions appear as Fourier coefficients of a meromorphic Jacobi form of negative definite matrix index. Hypergeometric $q$-series identities are also obtained.