- Title
- A modular supercongruence for ₆F₅: an Apéry-like story
- Creator
- Osburn, Robert; Straub, Armin; Zudilin, Wadim
- Relation
- Institut Fourier. Annales Vol. 68, Issue 5, p. 1987-2004
- Publisher Link
- http://dx.doi.org/10.5802/aif.3201
- Publisher
- Association des Annales de l'Institut Fourier
- Resource Type
- journal article
- Date
- 2018
- Description
- We prove a supercongruence modulo p³ between the pth Fourier coefficient of a weight 6 modular form and a truncated ₆F₅-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 relating the Apéry numbers to another Apéry-like sequence.
- Subject
- supercongruence; Apery numbers; Apery-like numbers; hypergeometric function
- Identifier
- http://hdl.handle.net/1959.13/1409150
- Identifier
- uon:35952
- Identifier
- ISSN:0373-0956
- Rights
- © Association des Annales de l’institut Fourier, 2018, Certains droits réservés. Cet article est mis à disposition selon les termes de la licence CREATIVE COMMONS ATTRIBUTION – PAS DE MODIFICATION 3.0 FRANCE. http://creativecommons.org/licenses/by-nd/3.0/fr/ © Association des Annales de l'stitut Fourier, 2018, Certain rights reserved. This item is made available under the terms of the license CREATIVE COMMONS ATTRIBUTION - NO MODIFICATION 3.0 FRANCE. http://creativecommons.org/licenses/by-nd/3.0/fr/
- Language
- eng
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