# Estimating the critical determinants of a class of three-dimensional star bodies

Communications in Mathematics (2017)

- Volume: 25, Issue: 2, page 149-157
- ISSN: 1804-1388

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topNowak, Werner Georg. "Estimating the critical determinants of a class of three-dimensional star bodies." Communications in Mathematics 25.2 (2017): 149-157. <http://eudml.org/doc/294547>.

@article{Nowak2017,

abstract = {In the problem of (simultaneous) Diophantine approximation in $\mathbb \{R\}^3$ (in the spirit of Hurwitz’s theorem), lower bounds for the critical determinant of the special three-dimensional body \[ K\_2:\quad (y^2+z^2)(x^2+y^2+z^2)\le 1 \]
play an important role; see [1], [6]. This article deals with estimates from below for the critical determinant $\Delta (K_c)$ of more general star bodies \[ K\_c:\quad (y^2+z^2)^\{c/2\}(x^2+y^2+z^2)\le 1, \]
where $c$ is any positive constant. These are obtained by inscribing into $K_c$ either a double cone, or an ellipsoid, or a double paraboloid, depending on the size of $c$.},

author = {Nowak, Werner Georg},

journal = {Communications in Mathematics},

keywords = {Geometry of numbers; critical determinant; simultaneous Diophantine approximation},

language = {eng},

number = {2},

pages = {149-157},

publisher = {University of Ostrava},

title = {Estimating the critical determinants of a class of three-dimensional star bodies},

url = {http://eudml.org/doc/294547},

volume = {25},

year = {2017},

}

TY - JOUR

AU - Nowak, Werner Georg

TI - Estimating the critical determinants of a class of three-dimensional star bodies

JO - Communications in Mathematics

PY - 2017

PB - University of Ostrava

VL - 25

IS - 2

SP - 149

EP - 157

AB - In the problem of (simultaneous) Diophantine approximation in $\mathbb {R}^3$ (in the spirit of Hurwitz’s theorem), lower bounds for the critical determinant of the special three-dimensional body \[ K_2:\quad (y^2+z^2)(x^2+y^2+z^2)\le 1 \]
play an important role; see [1], [6]. This article deals with estimates from below for the critical determinant $\Delta (K_c)$ of more general star bodies \[ K_c:\quad (y^2+z^2)^{c/2}(x^2+y^2+z^2)\le 1, \]
where $c$ is any positive constant. These are obtained by inscribing into $K_c$ either a double cone, or an ellipsoid, or a double paraboloid, depending on the size of $c$.

LA - eng

KW - Geometry of numbers; critical determinant; simultaneous Diophantine approximation

UR - http://eudml.org/doc/294547

ER -

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