Comparing Two Formulas for the Gross-Stark Units
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866918250719215616 |
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| author | Honnor, Matthew H. L. |
| author_facet | Honnor, Matthew H. L. |
| contents | Let $F$ be a totally real number field. Dasgupta conjectured an explicit $p$-adic analytic formula for the Gross-Stark units of $F$. In a later paper, Dasgupta-Spiess conjectured a cohomological formula for the principal minors and the characteristic polynomial of the Gross regulator matrix associated to a totally odd character of $F$. Dasgupta-Spiess conjectured that these conjectural formulas coincide for the diagonal entries of Gross regulator matrix. In this paper, we prove this conjecture when $F$ is a cubic field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_06402 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Comparing Two Formulas for the Gross-Stark Units Honnor, Matthew H. L. Number Theory 11R42 Let $F$ be a totally real number field. Dasgupta conjectured an explicit $p$-adic analytic formula for the Gross-Stark units of $F$. In a later paper, Dasgupta-Spiess conjectured a cohomological formula for the principal minors and the characteristic polynomial of the Gross regulator matrix associated to a totally odd character of $F$. Dasgupta-Spiess conjectured that these conjectural formulas coincide for the diagonal entries of Gross regulator matrix. In this paper, we prove this conjecture when $F$ is a cubic field. |
| title | Comparing Two Formulas for the Gross-Stark Units |
| topic | Number Theory 11R42 |
| url | https://arxiv.org/abs/2108.06402 |