Some q-supercongruences modulo the square and cube of a cyclotomic polynomial

Two q-supercongruences of truncated basic hypergeometric series containing two free parameters are established by employing specific identities for basic hypergeometric series. The results partly extend two q-supercongruences that were earlier conjectured by the same authors and involve q-supercongr...

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Detalles Bibliográficos
Autores principales: Guo, Victor J. W., Schlosser, Michael J.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2021
Materias:
Original Paper
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550663/
https://www.ncbi.nlm.nih.gov/pubmed/34776811
http://dx.doi.org/10.1007/s13398-021-01070-y
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author Guo, Victor J. W.
Schlosser, Michael J.
author_facet Guo, Victor J. W.
Schlosser, Michael J.
author_sort Guo, Victor J. W.
collection PubMed
description Two q-supercongruences of truncated basic hypergeometric series containing two free parameters are established by employing specific identities for basic hypergeometric series. The results partly extend two q-supercongruences that were earlier conjectured by the same authors and involve q-supercongruences modulo the square and the cube of a cyclotomic polynomial. One of the newly proved q-supercongruences is even conjectured to hold modulo the fourth power of a cyclotomic polynomial.
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spelling pubmed-85506632021-11-10 Some q-supercongruences modulo the square and cube of a cyclotomic polynomial Guo, Victor J. W. Schlosser, Michael J. Rev R Acad Cienc Exactas Fis Nat A Mat Original Paper Two q-supercongruences of truncated basic hypergeometric series containing two free parameters are established by employing specific identities for basic hypergeometric series. The results partly extend two q-supercongruences that were earlier conjectured by the same authors and involve q-supercongruences modulo the square and the cube of a cyclotomic polynomial. One of the newly proved q-supercongruences is even conjectured to hold modulo the fourth power of a cyclotomic polynomial. Springer International Publishing 2021-05-31 2021 /pmc/articles/PMC8550663/ /pubmed/34776811 http://dx.doi.org/10.1007/s13398-021-01070-y Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Original Paper
Guo, Victor J. W.
Schlosser, Michael J.
Some q-supercongruences modulo the square and cube of a cyclotomic polynomial
title Some q-supercongruences modulo the square and cube of a cyclotomic polynomial
title_full Some q-supercongruences modulo the square and cube of a cyclotomic polynomial
title_fullStr Some q-supercongruences modulo the square and cube of a cyclotomic polynomial
title_full_unstemmed Some q-supercongruences modulo the square and cube of a cyclotomic polynomial
title_short Some q-supercongruences modulo the square and cube of a cyclotomic polynomial
title_sort some q-supercongruences modulo the square and cube of a cyclotomic polynomial
topic Original Paper
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550663/
https://www.ncbi.nlm.nih.gov/pubmed/34776811
http://dx.doi.org/10.1007/s13398-021-01070-y
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