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

In this paper, three parametric q-supercongruences for truncated very-well-poised basic hypergeometric series are proved, one of them modulo the square, the other two modulo the cube of a cyclotomic polynomial. The main ingredients of proof include a basic hypergeometric summation by George Gasper,...

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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 2022
Materias:
Original Paper
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9573859/
https://www.ncbi.nlm.nih.gov/pubmed/36267679
http://dx.doi.org/10.1007/s13398-022-01338-x
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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 In this paper, three parametric q-supercongruences for truncated very-well-poised basic hypergeometric series are proved, one of them modulo the square, the other two modulo the cube of a cyclotomic polynomial. The main ingredients of proof include a basic hypergeometric summation by George Gasper, the method of creative microscoping (a method recently introduced by the first author in collaboration with Wadim Zudilin), and the Chinese remainder theorem for coprime polynomials.
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spelling pubmed-95738592022-10-18 Three families of 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 In this paper, three parametric q-supercongruences for truncated very-well-poised basic hypergeometric series are proved, one of them modulo the square, the other two modulo the cube of a cyclotomic polynomial. The main ingredients of proof include a basic hypergeometric summation by George Gasper, the method of creative microscoping (a method recently introduced by the first author in collaboration with Wadim Zudilin), and the Chinese remainder theorem for coprime polynomials. Springer International Publishing 2022-10-16 2023 /pmc/articles/PMC9573859/ /pubmed/36267679 http://dx.doi.org/10.1007/s13398-022-01338-x Text en © The Author(s) 2022 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.
Three families of q-supercongruences modulo the square and cube of a cyclotomic polynomial
title Three families of q-supercongruences modulo the square and cube of a cyclotomic polynomial
title_full Three families of q-supercongruences modulo the square and cube of a cyclotomic polynomial
title_fullStr Three families of q-supercongruences modulo the square and cube of a cyclotomic polynomial
title_full_unstemmed Three families of q-supercongruences modulo the square and cube of a cyclotomic polynomial
title_short Three families of q-supercongruences modulo the square and cube of a cyclotomic polynomial
title_sort three families of q-supercongruences modulo the square and cube of a cyclotomic polynomial
topic Original Paper
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9573859/
https://www.ncbi.nlm.nih.gov/pubmed/36267679
http://dx.doi.org/10.1007/s13398-022-01338-x
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