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arXiv · 1705.05586

Sequences, modular forms and cellular integrals

Dermot McCarthy·Robert Osburn·Armin Straub
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Abstract

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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Dermot McCarthy, Robert Osburn, Armin Straub. 2018-09-10. Sequences, modular forms and cellular integrals. https://doi.org/10.1017/s0305004118000774

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