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Sequences, modular forms and cellular integrals

Sequences, modular forms and cellular integrals
Dermot McCarthy, Robert Osburn, Armin Straub — Mathematical Proceedings of the Cambridge Philosophical Society — 2018

Abstract

It is well-known that the Apéry 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.

An extended abstract of this paper has been published in the book 2017 MATRIX Annals, which documents scientific activities at MATRIX in 2017.

@article{brownsequences-2018,
}