Robert Osburn, Armin Straub, Wadim Zudilin — Annales 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.Download
| Link | Size | Description | Hits |
|---|---|---|---|
| supercongruence-6f5.pdf | 306.21 KB | Preprint (PDF, 17 pages) | 1921 |
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},
}