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

A modular supercongruence for 6F5: An Apéry-like story
Robert Osburn, Armin Straub, Wadim Zudilin — Preprint — 2017

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.

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BibTeX

@article{supercongruence-6f5-2017,
    author = {Robert Osburn and Armin Straub and Wadim Zudilin},
    title = {A modular supercongruence for $_6F_5$: An Ap\'ery-like story},
    journal = {Preprint},
    year = {2017},
}