A Minkowski-type theorem on distances to cusps: the general case
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908610119860224 |
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| author | Dutour, Mathieu |
| author_facet | Dutour, Mathieu |
| contents | In a previous paper, we studied the connection between points in $\mathbb{H}^n$ and $2$-dimensional rigid adelic spaces on a totally real number field $K$ with class number $h_K = 1$. This last assumption was needed to link heights and distances to cusps. In this paper, we remove this hypothesis to obtain, without restriction on $K$ totally real, an analogue of Minkowski's second theorem on the Roy--Thunder minima of a $2$-dimensional rigid adelic space in the framework of distances between a point $τ\in \mathbb{H}^n$ and its two closest cusps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21492 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Minkowski-type theorem on distances to cusps: the general case Dutour, Mathieu Number Theory 11F41 In a previous paper, we studied the connection between points in $\mathbb{H}^n$ and $2$-dimensional rigid adelic spaces on a totally real number field $K$ with class number $h_K = 1$. This last assumption was needed to link heights and distances to cusps. In this paper, we remove this hypothesis to obtain, without restriction on $K$ totally real, an analogue of Minkowski's second theorem on the Roy--Thunder minima of a $2$-dimensional rigid adelic space in the framework of distances between a point $τ\in \mathbb{H}^n$ and its two closest cusps. |
| title | A Minkowski-type theorem on distances to cusps: the general case |
| topic | Number Theory 11F41 |
| url | https://arxiv.org/abs/2510.21492 |