Sequences, modular forms and cellular integrals

Sequences, modular forms and cellular integrals
Dermot McCarthy, Robert Osburn, Armin Straub — Preprint — 2017


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 abstract of this paper will appear in the book 2017 MATRIX Annals, which documents scientific activities at MATRIX in 2017.


383.28 KB Preprint (PDF, 26 pages) 349


    author = {Dermot McCarthy and Robert Osburn and Armin Straub},
    title = {Sequences, modular forms and cellular integrals},
    journal = {Preprint},
    year = {2017},