Some $q$-supercongruences for multiple basic hypergeometric series
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866909286557286400 |
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| author | Wei, Chuanan |
| author_facet | Wei, Chuanan |
| contents | In terms of several summation and transformation formulas for basic hypergeometric series, two forms of the Chinese remainder theorem for coprime polynomials, the creative microscoping method introduced by Guo and Zudilin, Guo and Li's lemma, and El Bachraoui's lemma, we establish some $q$-supercongruences for multiple basic hypergeometric series modulo the fifth and sixth powers of a cyclotomic polynomial. In detail, we generalize Guo and Li's two $q$-supercongruences for double basic hypergeometric series, which are related to $q$-analogues of Van Hamme's (C.2) supercongruence and Long's supercongruence, respectively. In addition, we also present two conclusions for double and triple hypergeometric series associated with Van Hamme's (D.2) supercongruence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07226 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some $q$-supercongruences for multiple basic hypergeometric series Wei, Chuanan Combinatorics In terms of several summation and transformation formulas for basic hypergeometric series, two forms of the Chinese remainder theorem for coprime polynomials, the creative microscoping method introduced by Guo and Zudilin, Guo and Li's lemma, and El Bachraoui's lemma, we establish some $q$-supercongruences for multiple basic hypergeometric series modulo the fifth and sixth powers of a cyclotomic polynomial. In detail, we generalize Guo and Li's two $q$-supercongruences for double basic hypergeometric series, which are related to $q$-analogues of Van Hamme's (C.2) supercongruence and Long's supercongruence, respectively. In addition, we also present two conclusions for double and triple hypergeometric series associated with Van Hamme's (D.2) supercongruence. |
| title | Some $q$-supercongruences for multiple basic hypergeometric series |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2408.07226 |