# Searching for modular companions

## TL;DR

This paper reports on a computational search for modular companions to specific q-series identities and conjectures, using asymptotic conditions from Nahm sums, focusing on Capparelli's identities and related partition conjectures.

## Contribution

It introduces a novel computational approach to identify modular companions for particular q-series identities based on Nahm sum asymptotics.

## Key findings

- Identified potential modular companions to Capparelli's identities.
- Found possible modular counterparts to certain partition conjectures.
- Provided computational evidence supporting the existence of modular relations.

## Abstract

In this note, we report on the results of a computer search performed to find possible modular companions to certain $q$-series identities and conjectures. For the search, we use conditions arising from the asymptotics of Nahm sums. We focus on two sets of identities: Capparelli's identities, and certain partition conjectures made by the author jointly with Matthew C. Russell.