頁籤選單縮合
題名 | A Counter Example for GLY Conjecture on Counting the Number of Integral Points in a 7-dimensional Tetrahedra |
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作者 | 林克保; 丘成棟; | 書刊名 | 長庚科技學刊 |
卷期 | 3 2004.12[民93.12] |
頁次 | 頁303-313 |
分類號 | 319.5 |
關鍵詞 | |
語文 | 英文(English) |
英文摘要 | Recently there has been tremendous interest in counting the number of integral points in n-dimensional tetrahedra with non-integral vertice due to its applications in primality testing and factoring in number theory and in singularities theory. In [Li-Ya 1] we propose a conjecture on sharp upper estimate of the number of integral points in n-dimensional tetrahedra with non-integral vertice. We show that this conjecture is true for dimension n = 3, 4, 5 cases as well as in the case of homogeneous n-dimensional tetrahedra. In this paper we review the GLY conjecture first, then we propose a counter example for GLY Conjecture on counting the number of integral points in a 7-dimensional tetrahedra. This counter example shows our conjecture need some modification to make it true for all possible tetrahedra, it also gives us some guidance to modify our conjecture. |
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