Mathematics > Number Theory
[Submitted on 11 May 2018 (v1), last revised 31 May 2019 (this version, v3)]
Title:On a question of Schmidt and Summerer concerning $3$-systems
View PDFAbstract: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.
Submission history
From: Johannes Schleischitz [view email][v1] Fri, 11 May 2018 16:31:42 UTC (8 KB)
[v2] Thu, 27 Dec 2018 10:42:24 UTC (10 KB)
[v3] Fri, 31 May 2019 07:41:40 UTC (9 KB)
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