تقرير
Counter-examples in Parametric Geometry of Numbers
| العنوان: | Counter-examples in Parametric Geometry of Numbers |
|---|---|
| المؤلفون: | Rivard-Cooke, Martin, Roy, Damien |
| المصدر: | Acta Arithmetica, vol. 196.3 (2020), 303-323 |
| سنة النشر: | 2019 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, 11J13 (Primary), 11J82 (Secondary) |
| الوصف: | Thanks to recent advances in parametric geometry of numbers, we know that the spectrum of any set of $m$ exponents of Diophantine approximation to points in $\mathbb{R}^n$ (in a general abstract setting) is a compact connected subset of $\mathbb{R}^m$. Moreover, this set is semi-algebraic and closed under coordinate-wise minimum for $n\le 3$. In this paper, we give examples showing that for $n\ge 4$ each of the latter properties may fail. Comment: 18 pages, 5 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1912.06483 |
| رقم الأكسشن: | edsarx.1912.06483 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |