Mixed motives and linear forms in the Catalan constant
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918307156721664 |
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| author | Eskandari, Payman Murty, Kumar Nemoto, Yusuke |
| author_facet | Eskandari, Payman Murty, Kumar Nemoto, Yusuke |
| contents | We first give a geometric construction of a 2-dimensional mixed motive over $\mathbb{Q}$ with the Catalan constant $\mathbf{G}=1-1/3^2+1/5^2-1/7^2+\cdots$ as a period. We then use this motive to obtain a supply of linear forms in 1 and $\mathbf{G}$. We also explicitly compute the coefficients of 1 and $\mathbf{G}$ in these linear forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20648 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mixed motives and linear forms in the Catalan constant Eskandari, Payman Murty, Kumar Nemoto, Yusuke Number Theory Algebraic Geometry 11G99, 11M06, 14F42 We first give a geometric construction of a 2-dimensional mixed motive over $\mathbb{Q}$ with the Catalan constant $\mathbf{G}=1-1/3^2+1/5^2-1/7^2+\cdots$ as a period. We then use this motive to obtain a supply of linear forms in 1 and $\mathbf{G}$. We also explicitly compute the coefficients of 1 and $\mathbf{G}$ in these linear forms. |
| title | Mixed motives and linear forms in the Catalan constant |
| topic | Number Theory Algebraic Geometry 11G99, 11M06, 14F42 |
| url | https://arxiv.org/abs/2510.20648 |