Some supercongruences of arbitrary length

Frits Beukers; Eric Delaygue

doi:10.1016/j.indag.2022.04.002

Some supercongruences of arbitrary length

Frits Beukers^*
, Eric Delaygue

^*Corresponding author for this work

Universite Claude Bernard Lyon 1

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

We prove supercongruences modulo p² for values of truncated hypergeometric series at some special points. The parameters of the hypergeometric series are d copies of 1/2 and d copies of 1 for any integer d≥2. In addition we describe their relation to hypergeometric motives.

Original language	English
Pages (from-to)	946-955
Number of pages	10
Journal	Indagationes Mathematicae
Volume	33
Issue number	5
DOIs	https://doi.org/10.1016/j.indag.2022.04.002
Publication status	Published - Sept 2022

Bibliographical note

Funding Information:
The authors would like to thank the Matrix Institute and the organizers of the workshop Hypergeometric Motives and Calabi–Yau Differential Equations for the wonderful and stimulating environment in which this research arose. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme under the Grant Agreement No 648132.

Funding Information:
The authors would like to thank the Matrix Institute and the organizers of the workshop Hypergeometric Motives and Calabi–Yau Differential Equations for the wonderful and stimulating environment in which this research arose. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under the Grant Agreement No 648132 .

Publisher Copyright:
© 2022 The Author(s)

Funding

The authors would like to thank the Matrix Institute and the organizers of the workshop Hypergeometric Motives and Calabi–Yau Differential Equations for the wonderful and stimulating environment in which this research arose. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme under the Grant Agreement No 648132. The authors would like to thank the Matrix Institute and the organizers of the workshop Hypergeometric Motives and Calabi–Yau Differential Equations for the wonderful and stimulating environment in which this research arose. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under the Grant Agreement No 648132 .

Keywords

Hypergeometric series
Super congruence
Unit root
Zeta function

Access to Document

10.1016/j.indag.2022.04.002Licence: CC BY

1-s2.0-S0019357722000258-mainFinal published version, 272 KBLicence: CC BY

Cite this

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KW - Unit root

KW - Zeta function

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Some supercongruences of arbitrary length

Abstract

Bibliographical note

Funding

Keywords

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