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Title: On a question of Schmidt and Summerer concerning $3$-systems (English)
Author: Schleischitz, Johannes
Language: English
Journal: Communications in Mathematics
ISSN: 1804-1388 (print)
ISSN: 2336-1298 (online)
Volume: 28
Issue: 3
Year: 2020
Pages: 253-262
Summary lang: English
Category: math
Summary: Following a suggestion of W.M. Schmidt and L. Summerer, we construct a proper $3$-system $(P_{1},P_{2},P_{3})$ with the property $\overline {\varphi }_{3}=1$. In fact, our method generalizes to provide $n$-systems with $\overline {\varphi }_{n}=1$, for arbitrary $n\geq 3$. We visualize our constructions with graphics. We further present explicit examples of numbers $\xi _{1}, \ldots , \xi _{n-1}$ that induce the $n$-systems in question. (English)
Keyword: parametric geometry of numbers
Keyword: simultaneous approximation
MSC: 11H06
MSC: 11J13
idZBL: Zbl 1475.11131
idMR: MR4197077
Date available: 2021-03-03T08:55:16Z
Last updated: 2022-04-28
Stable URL:
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