AI Article Synopsis
- - The paper establishes three parametric supercongruences related to truncated very-well-poised basic hypergeometric series, with one proven modulo a square and the others modulo the cube of a cyclotomic polynomial.
- - Key proof techniques involve a basic hypergeometric summation attributed to George Gasper, the creative microscoping method recently introduced by the authors, and the application of the Chinese remainder theorem for coprime polynomials.
- - These results contribute to the field of hypergeometric series and number theory, showcasing innovative connections between series and polynomial congruences.
Article Abstract
In this paper, three parametric -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.
Download full-text PDF |
Source |
|---|---|
| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC9573859 | PMC |
| http://dx.doi.org/10.1007/s13398-022-01338-x | DOI Listing |
Publication Analysis
Top Keywords
modulo square
8
cube cyclotomic
8
cyclotomic polynomial
8
basic hypergeometric
8
three families
4
families -supercongruences
4
-supercongruences modulo
4
square cube
4
polynomial paper
4
paper three
4
Similar Publications
Want AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!