# On the convergence of certain indefinite theta series

## TL;DR

This paper provides an elementary proof of the convergence of indefinite theta series in signature (n,2) and establishes the necessity of certain incidence conditions for convergence.

## Contribution

It offers a new elementary proof for the convergence of indefinite theta series and proves that the incidence conditions are necessary for convergence.

## Key findings

- Elementary proof of convergence for indefinite theta series.
- Incidence conditions are necessary for convergence.
- Clarifies conditions for convergence in signature (n,2).

## Abstract

We give an elementary proof of the convergence of indefinite theta series associated to an inner space of signature $(n,2)$ conjectured in the work of Alexandrov,Banerjee,Manschot and Pioline (2018) and show that the incidence conditions are also necessary for the convergence.