Back to Search
Start Over
$q$-Supercongruences with parameters
- Publication Year :
- 2020
-
Abstract
- In terms of the creative microscoping method recently introduced by Guo and Zudilin [Adv. Math. 346 (2019), 329--358], we find a $q$-supercongruence with four parameters modulo $\Phi_n(q)(1-aq^n)(a-q^n)$, where $\Phi_n(q)$ denotes the $n$-th cyclotomic polynomial in $q$. Then we empoly it and the Chinese remainder theorem for coprime polynomials to derive a $q$-supercongruence with two parameters modulo $[n]\Phi_n(q)^3$, where $[n]=(1-q^n)/(1-q)$ is the $q$-integer.<br />Comment: arXiv admin note: text overlap with arXiv:2005.14196
- Subjects :
- Mathematics - Combinatorics
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2010.02025
- Document Type :
- Working Paper