On a question of Schmidt and Summerer concerning $3$-systems

Schleischitz, Johannes. "On a question of Schmidt and Summerer concerning $3$-systems." Communications in Mathematics 28.3 (2020): 253-262. <http://eudml.org/doc/297153>.

@article{Schleischitz2020,
abstract = {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 $n\ge 3$. 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.},
author = {Schleischitz, Johannes},
journal = {Communications in Mathematics},
keywords = {parametric geometry of numbers; simultaneous approximation},
language = {eng},
number = {3},
pages = {253-262},
publisher = {University of Ostrava},
title = {On a question of Schmidt and Summerer concerning $3$-systems},
url = {http://eudml.org/doc/297153},
volume = {28},
year = {2020},
}

TY - JOUR
AU - Schleischitz, Johannes
TI - On a question of Schmidt and Summerer concerning $3$-systems
JO - Communications in Mathematics
PY - 2020
PB - University of Ostrava
VL - 28
IS - 3
SP - 253
EP - 262
AB - 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 $n\ge 3$. 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.
LA - eng
KW - parametric geometry of numbers; simultaneous approximation
UR - http://eudml.org/doc/297153
ER -