Ranks of Matrices of Logarithms of Algebraic Numbers II: The Matrix Coefficient Conjecture
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910566698713088 |
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| author | Dasgupta, Samit Kakde, Mahesh |
| author_facet | Dasgupta, Samit Kakde, Mahesh |
| contents | Many questions in number theory concern the nonvanishing of determinants of square matrices of logarithms (complex or p-adic) of algebraic numbers. We present a new conjecture that states that if such a matrix has vanishing determinant, then after a rational change of basis on the left and right, it can be made to have a vanishing coefficient. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08178 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ranks of Matrices of Logarithms of Algebraic Numbers II: The Matrix Coefficient Conjecture Dasgupta, Samit Kakde, Mahesh Number Theory 11J81, 11R27 Many questions in number theory concern the nonvanishing of determinants of square matrices of logarithms (complex or p-adic) of algebraic numbers. We present a new conjecture that states that if such a matrix has vanishing determinant, then after a rational change of basis on the left and right, it can be made to have a vanishing coefficient. |
| title | Ranks of Matrices of Logarithms of Algebraic Numbers II: The Matrix Coefficient Conjecture |
| topic | Number Theory 11J81, 11R27 |
| url | https://arxiv.org/abs/2408.08178 |