AI Article Synopsis
- - The text discusses the establishment of two new supercongruences related to truncated basic hypergeometric series with two free parameters, using identities specific to these series.
- - These results expand on previously conjectured supercongruences linked to cyclotomic polynomials, particularly involving modular properties modulo the square and cube.
- - One of the newly proved supercongruences is suggested to potentially hold true without exception when considered modulo the fourth power of a cyclotomic polynomial.
Article Abstract
Two -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 -supercongruences that were earlier conjectured by the same authors and involve -supercongruences modulo the square and the cube of a cyclotomic polynomial. One of the newly proved -supercongruences is even conjectured to hold modulo the fourth power of a cyclotomic polynomial.
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Source |
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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550663 | PMC |
| http://dx.doi.org/10.1007/s13398-021-01070-y | DOI Listing |
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