| Romanoff定理的定量形式 |
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| 引用本文： | 孙学功,陈永高.Romanoff定理的定量形式[J].数学学报,2006,49(3):577-582. |
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| 作者姓名： | 孙学功 陈永高 |
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| 作者单位： | [1]淮海工学院数理系,连云港222005 [2]南京师范大学数学与计算机科学学院,南京210097 |
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| 基金项目： | 国家自然科学基金资助项目（10471064,10171046） |
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| 摘 要： | 1934年,Romanoff证明了能表成2的方幂与一个素数之和形式的正整数在正整数集合中有正的比例．最近,本文作者证明了对充分大的x,能表成2的方幂与一个素数之和形式的正整数在不超过x的正整数中至少有0．0868x个．本文证明了:设 x≥5,则在不超过x的正整数中,能表成2的方幂与一个素数之和的数的个数不少于 0．005x,即给出了Romanoff定理的定量形式．
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| 关 键 词： | Romanoff定理 Selberg筛法 素数 |
| 文章编号： | 0583-1431（2006）03-0577-06 |
| 收稿时间： | 2004-09-27 |
| 修稿时间： | 2004-09-272005-03-20 |
On Quantitative Romanoff's Theorem |
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| Xue Gong SUN.On Quantitative Romanoff''s Theorem[J].Acta Mathematica Sinica,2006,49(3):577-582. |
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| Authors: | Xue Gong SUN |
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| Institution: | Department of Mathematics and Science, Huai Hal Institute of Technology Lianyun Gang 222005, P. R. China Yong Gao CHEN School of Mathematics and Computor Science, Nanjing Normal University Nanjing 210097, P. R. China |
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| Abstract: | In 1934, Romanoff proved that there are positive proportion natural numbers which can be expressed as a sum of a prime and a power of 2. Recently, the authors proved that for all sufficiently larger x, the proportion is large than 0.0868. In this paper,a quantitative version of Romanoff's Theorem is given. The following result is proved: For all x≥5, the proportion of natural numbers which can be expressed as a sum of a prime and a power of 2 is larger than 0.005. |
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| Keywords: | Romanoff's theorem Selberg sieve prime |
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