Sequences, modular forms and cellular integrals
Number Theory
2020-02-19 v2 Algebraic Geometry
Combinatorics
Abstract
It is well-known that the Ap\'ery sequences which arise in the irrationality proofs for and satisfy many intriguing arithmetic properties and are related to the 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.
Cite
@article{arxiv.1705.05586,
title = {Sequences, modular forms and cellular integrals},
author = {Dermot McCarthy and Robert Osburn and Armin Straub},
journal= {arXiv preprint arXiv:1705.05586},
year = {2020}
}
Comments
26 pages, to appear in Mathematical Proceedings of the Cambridge Philosophical Society