| Title:
|
Estimating the critical determinants of a class of three-dimensional star bodies (English) |
| Author:
|
Nowak, Werner Georg |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 |
| Volume:
|
25 |
| Issue:
|
2 |
| Year:
|
2017 |
| Pages:
|
149-157 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $c$. (English) |
| Keyword:
|
Geometry of numbers; critical determinant; simultaneous Diophantine approximation |
| MSC:
|
11H16 |
| MSC:
|
11J13 |
| idZBL:
|
Zbl 06888205 |
| idMR:
|
MR3745434 |
| . |
| Date available:
|
2018-02-05T14:42:41Z |
| Last updated:
|
2020-01-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147063 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
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| . |
