# Sequences, modular forms and cellular integrals

## TL;DR

This paper explores the link between sequences from cellular integrals and modular forms, extending known properties of Apéry sequences and proposing a conjecture on supercongruences.

## Contribution

It demonstrates that sequences from Brown's cellular integrals are connected to modular forms and formulates a new conjecture on supercongruences.

## Key findings

- Sequences from cellular integrals relate to modular forms.
- The connection extends properties known for Apéry sequences.
- A conjecture on supercongruences is proposed.

## Abstract

It is well-known that the Ap\'ery sequences which arise in the irrationality proofs for $\zeta(2)$ and $\zeta(3)$ satisfy many intriguing arithmetic properties and are related to the $p$th Fourier coefficients of modular forms. In this paper, we prove that the connection to modular forms persists for sequences associated to Brown's cellular integrals and state a general conjecture concerning supercongruences.