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arXiv · 1701.04098

A modular supercongruence for $_6F_5$: an Apéry-like story

Robert Osburn·Armin Straub·Wadim Zudilin
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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 $ζ(3)$ 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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Robert Osburn, Armin Straub, Wadim Zudilin. 2017-11-15. A modular supercongruence for $_6F_5$: an Apéry-like story. https://doi.org/10.5802/aif.3201

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