English

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 ζ(2)\zeta(2) and ζ(3)\zeta(3) satisfy many intriguing arithmetic properties and are related to the ppth 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.

Keywords

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