Sequences, modular forms and cellular integrals

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.

26 pages, to appear in Mathematical Proceedings of the Cambridge Philosophical Society

References in corpus (2)

• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Interpolated sequences and critical $L$-values of modular forms

Cited by in corpus (3)

• Interpolated sequences and critical $L$-values of modular forms
• Distribution of values of Gaussian hypergeometric functions
• On sporadic sequences