$q$-Supercongruences for multidimensional series modulo the sixth power of a cyclotomic polynomial
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913458355699712 |
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| author | Wei, Chuanan |
| author_facet | Wei, Chuanan |
| contents | With the help of El Bachraoui's lemma, the creative microscoping method, and a new form of the Chinese remainder theorem for coprime polynomials, we prove a $q$-supercongruence for double series and a $q$-supercongruence for triple series modulo the sixth power of a cyclotomic polynomial. As conclusions, two corresponding supercongruences for double and triple series, which are associated with the (D.2) supercongruence of Van Hamme, are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02002 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $q$-Supercongruences for multidimensional series modulo the sixth power of a cyclotomic polynomial Wei, Chuanan Combinatorics Number Theory With the help of El Bachraoui's lemma, the creative microscoping method, and a new form of the Chinese remainder theorem for coprime polynomials, we prove a $q$-supercongruence for double series and a $q$-supercongruence for triple series modulo the sixth power of a cyclotomic polynomial. As conclusions, two corresponding supercongruences for double and triple series, which are associated with the (D.2) supercongruence of Van Hamme, are given. |
| title | $q$-Supercongruences for multidimensional series modulo the sixth power of a cyclotomic polynomial |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2408.02002 |