The Modularity of Z.-W. Sun's Conjectural Formulas for $\frac{1}π$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916465631821824 |
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| author | van Hoeij, Mark Tsai, Wei-Lun Ye, Dongxi |
| author_facet | van Hoeij, Mark Tsai, Wei-Lun Ye, Dongxi |
| contents | In this work, we establish modular parameterizations for two general formulas for $\frac{1}π$ that subsume conjectural Ramanujan type formulas due to Z.-W. Sun, which have remained open since 2011. As an application of this, in a conceptual way we interpret how Sun's conjectural formulas arise and can be verified, as well as recover other cases that were proved by Cooper, Wan and Zudilin. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_19289 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Modularity of Z.-W. Sun's Conjectural Formulas for $\frac{1}π$ van Hoeij, Mark Tsai, Wei-Lun Ye, Dongxi Number Theory 11F03, 11Y60, 33C05 In this work, we establish modular parameterizations for two general formulas for $\frac{1}π$ that subsume conjectural Ramanujan type formulas due to Z.-W. Sun, which have remained open since 2011. As an application of this, in a conceptual way we interpret how Sun's conjectural formulas arise and can be verified, as well as recover other cases that were proved by Cooper, Wan and Zudilin. |
| title | The Modularity of Z.-W. Sun's Conjectural Formulas for $\frac{1}π$ |
| topic | Number Theory 11F03, 11Y60, 33C05 |
| url | https://arxiv.org/abs/2410.19289 |