TY - JOUR
T1 - Sequences, modular forms and cellular integrals
AU - McCarthy, Dermot
AU - Osburn, Robert
AU - Straub, Armin
N1 - Funding Information:
Acknowledgements. The first and third authors are supported by a grant from the Si-mons Foundation (#353329, Dermot McCarthy; #514645, Armin Straub). The second author would like to thank both the Institut des Hautes Études Scientifiques and the Max–Planck-Institut für Mathematik for their support and Francis Brown for his encouragement during the initial stages of this project. He also thanks the organisers of the workshop “Hypergeometric motives and Calabi-Yau differential equations”, January 8–27, 2017 at the MATRIX institute, The University of Melbourne at Creswick, for the opportunity to discuss these results. The authors are grateful to Clément Dupont for several insightful and helpful comments on cellular integrals.
Publisher Copyright:
Copyright © Cambridge Philosophical Society 2018.
PY - 2020/3/1
Y1 - 2020/3/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85054953289&partnerID=8YFLogxK
U2 - 10.1017/S0305004118000774
DO - 10.1017/S0305004118000774
M3 - Article
AN - SCOPUS:85054953289
SN - 0305-0041
VL - 168
SP - 379
EP - 404
JO - Mathematical Proceedings of the Cambridge Philosophical Society
JF - Mathematical Proceedings of the Cambridge Philosophical Society
IS - 2
ER -