Sequences, modular forms and cellular integrals

It is well-known that the Apéry sequences which arise in the irrationality proofs for $ζ(2)$ and $ζ(3)$ 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.

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