Saved in:
Bibliographic Details
Main Author: Dutour, Mathieu
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2510.21492
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866908610119860224
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