| 五个具有固定素因子个数的整数之平方和 |
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| 引用本文： | 孟宪萌.五个具有固定素因子个数的整数之平方和[J].数学学报,2006,49(1):119-128. |
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| 作者姓名： | 孟宪萌 |
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| 作者单位： | 山东财政学院统计与数理学院,济南250014 |
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| 基金项目： | 山东省教育厅科研基金资助项目（03F06）;山东财政学院博士基金资助项目 |
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| 摘 要： | 设N≡5(mod24)为充分大的正整数,若GRH(广义Riemann假设)成立, 则方程N=n12+n22+…+n52有解,此处ni,i=1,2,…,5具有固定素因子个数,并且方程解数具有渐近式．
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| 关 键 词： | 指数和 圆法 堆垒素数论 |
| 文章编号： | 0583-1431（2006）01-0119-10 |
| 收稿时间： | 2003-01-17 |
| 修稿时间： | 2003-01-172004-12-13 |
On Sums of Five Squares with a Fixed Numbes of Prime Factors |
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| Xian Meng MENG.On Sums of Five Squares with a Fixed Numbes of Prime Factors[J].Acta Mathematica Sinica,2006,49(1):119-128. |
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| Authors: | Xian Meng MENG |
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| Institution: | Xian Meng MENG Department of Statistics and Mathematics,Shandong Financel Institute, Jinan 250014, P. R. China |
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| Abstract: | Let N≡ 5 (mod 24) be a sufficiently large positive integer. Assume GRH (the generalized Riemann hypothesis), then the equation N = n_1~2+ n_2~2+…+ n_2~5 has solutions, where ni, i = 1,2,..., 5 has a fixed number of prime factors. Puthermore, an asymptotic formula for the number of solutions is obtained. |
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| Keywords: | exponential sum circle method additive problem |
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