A discrete analogue for Minkowski’s second theorem on successive minima
The main result of this paper is an inequality relating the lattice point enumerator of a 3-dimensional, 0-symmetric convex body and its successive minima. This is an example of generalization of Minkowski's theorems on successive minima, where the volume is replaced by the discrete analogue, t...
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| التنسيق: | مقال |
| اللغة: | English |
| منشور في: |
2013
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| الموضوعات: | |
| الوصول للمادة أونلاين: | https://hdl.handle.net/10356/98234 http://hdl.handle.net/10220/12320 |
| الوسوم: |
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| المؤسسة: | Nanyang Technological University |
| اللغة: | English |
| الملخص: | The main result of this paper is an inequality relating the lattice point enumerator of a 3-dimensional, 0-symmetric convex body and its successive minima. This is an example of generalization of Minkowski's theorems on successive minima, where the volume is replaced by the discrete analogue, the lattice point enumerator. This problem is still open in higher dimensions, however, we introduce a stronger conjecture that shows a possibility of proof by induction on the dimension. |
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