| 3个素数平方和的非线性型的整数部分 |
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| 引用本文： | 李伟平,王天泽. 3个素数平方和的非线性型的整数部分[J]. 数学年刊A辑(中文版), 2011, 32(6): 753-762 |
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| 作者姓名： | 李伟平 王天泽 |
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| 作者单位： | 河南财经政法大学数学与信息科学系;华北水利水电学院数学与信息科学学院; |
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| 基金项目： | 国家自然科学基金(No11071070); 河南省教育厅自然科学研究计划(No2011B110002)资助的项目 |
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| 摘 要： | 假设λ,μ,υ是不全为负的非零实数,λ是无理数,k是正整数,则存在无穷多素数p_1,p_2,p_,p,3使得[λp_1~2+μp_2~2+υp_3~2]=kp.特别地,[λp_1~2+μp_2~2+υp_3~2]表示无穷多素数.
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| 关 键 词： | 素数 非线性型 Davenport-Heilbronn方法 |
Integral Part of a Nonlinear Form with Three Squares of Primes |
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| LI Weiping and WANG Tianze. Integral Part of a Nonlinear Form with Three Squares of Primes[J]. Chinese Annals of Mathematics, 2011, 32(6): 753-762 |
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| Authors: | LI Weiping and WANG Tianze |
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| Affiliation: | LI Weiping~1 WANG Tianze~2 1 Department of Mathematics and Information Science,Henan University of Economics and Law,Zhengzhou 450002.China. 2 School of Mathematics and Information Science,North China University of Water Conservancy and Electric Power,Zhengzhou 450011,China. |
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| Abstract: | It is shown that if $lambda,mu,nu$ are non-zero real numbers,at least one of which is non-negative, $lambda$ is irrational, and $k$ is a positive integer, then there exist infinite primes $p_1, p_2, p_3, p$, such that$$[lambda p_1^2+mu p_2^2+nu p_3^2]=kp.$$ In particular, $[lambda p_1^2+mu p_2^2+nu p_3^2]$ represents infinite primes. |
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| Keywords: | Prime Nonlinear form Davenport-Heilbronn method |
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