A modular supercongruence for $_6F_5$: an Ap\'ery-like story
Number Theory
2021-02-04 v2 Combinatorics
Abstract
We prove a supercongruence modulo between the th Fourier coefficient of a weight 6 modular form and a truncated -hypergeometric series. Novel ingredients in the proof are the comparison of two rational approximations to to produce non-trivial harmonic sum identities and the reduction of the resulting congruences between harmonic sums via a congruence between the Ap\'ery numbers and another Ap\'ery-like sequence.
Keywords
Cite
@article{arxiv.1701.04098,
title = {A modular supercongruence for $_6F_5$: an Ap\'ery-like story},
author = {Robert Osburn and Armin Straub and Wadim Zudilin},
journal= {arXiv preprint arXiv:1701.04098},
year = {2021}
}
Comments
17 pages, to appear in Annales de l'Institut Fourier (Grenoble)