| 关于Diophantine m-tuples的个数(英文) |
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| 引用本文： | 劳会学.关于Diophantine m-tuples的个数(英文)[J].数学进展,2010(3). |
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| 作者姓名： | 劳会学 |
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| 作者单位： | 山东师范大学数学科学学院;山东大学数学与系统科学学院; |
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| 基金项目： | supported by the NSFC(No.10701048) |
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| 摘 要： | 对于一个由m个正整数构成的数组,若其中任意两个正整数的乘积都等于一个完全平方数减去1,则称这个数组为Diophantine m-tuples.最近,Dujella获得了关于Diophantine2-tuples及3-tuples个数的渐进公式.本文改进了的相关结果.
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| 关 键 词： | Diophantine m-tuples 渐进公式 除数函数 |
On the Number of Diophantine m-tuples |
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| LAO Huixue.On the Number of Diophantine m-tuples[J].Advances in Mathematics,2010(3). |
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| Authors: | LAO Huixue |
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| Institution: | LAO Huixue (1.School of Math.Science,Shandong Normal Univ.,Jinan,Shandong,250014,P.R.China,2.School of Math,and System Sciences,Shandong Univ.,250100,P.R.China) |
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| Abstract: | A set of m positive integers is called a Diophantine m-tuple if the product of any two of them is one less than a perfect square.Recently Dujella derived asymptotic estimates for the number of Diophantine pairs and triples.In this paper we establish some more explicit asymptotic formulas. |
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| Keywords: | Diophantine m-tuple asymptotic formula divisor function |
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