arminstraub.com

# A modular supercongruence for 6F5: An Apéry-like story

A modular supercongruence for 6F5: An Apéry-like story
Robert Osburn, Armin Straub, Wadim ZudilinAnnales de l'Institut Fourier — Volume 68, Number 5, 2018, Pages 1987-2004

## Abstract

We prove a supercongruence modulo $$p^3$$ between the $$p$$th Fourier coefficient of a weight 6 modular form and a truncated $$_6F_5$$-hypergeometric series. Novel ingredients in the proof are the comparison of two rational approximations to $$\zeta(3)$$ to produce non-trivial harmonic sum identities and the reduction of the resulting congruences between harmonic sums via a congruence between the Apéry numbers and another Apéry-like sequence.

306.21 KB Preprint (PDF, 17 pages) 774

## BibTeX

@article{supercongruence-6f5-2018,
author = {Robert Osburn and Armin Straub and Wadim Zudilin},
title = {A modular supercongruence for $_6F_5$: An Ap\'ery-like story},
journal = {Annales de l'Institut Fourier},
year = {2018},
volume = {68},
number = {5},
pages = {1987--2004},
doi = {10.5802/aif.3201},
}