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 pth 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.
MSC Codes 11F03 (Primary), 11M32, 14H10 (Secondary)
|State||Published - May 16 2017|
- Modular forms
- Period integrals