| 李伟平,王天泽.特殊集上素变数方程的解[J].数学年刊A辑,2014,35(1):109~114 |
| 特殊集上素变数方程的解 |
| Solutions to Equations with Prime Variables in a Special Set |
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| DOI： |
| 中文关键词: 素数, Goldbach型问题, 二进制展开式 |
| 英文关键词:Prime, Goldbach's problem, Binary expansion |
| 基金项目:国家自然科学基金 (No.11071070)和河南省教育厅自然科学研究计划 (No.2011B110002) |
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| 中文摘要: |
| 令$n=e_0+e_12+\cdots +e_k2^k$, 其中$e_j=0,1\ (j=0,\cdots,k)$
表示自然数$n$的二进制展开式, $ \mathbb{N}_0$ 表示二进制展开式中项数为偶数的自然数的集合.分别给出了这个特殊集上素变数方程 $p_1+p_2+p_3^k=N$和
$p_1+p_2^2+p_3^2+p_4^2=N$解的个数的渐近公式. |
| 英文摘要: |
| Let $n=e_0+e_12+\cdots+e_k2^k$, where $e_j=0,1\ (j=0,\cdots,k)$ be a binary expansion of a natural number $n$.
Let $\mathbb{N}_0$ be a class of natural numbers whose binary expansions contain even items.
Representable asymptotic formulae on the number of solutions to prime variable equations
$p_1 + p_2 + p^k_3 = N$ and $p_1 + p^2_2+ p^2_3+ p^2_4= N$ in the set $N_0$ are obtained, respectively. |
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