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《Acta Mathematica Sinica(Chinese Series)》 2019-01
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Diophantine Approximation with Prime Variables and Mixed Powers

Wei Ping LI;Wen Xu GE;Tian Ze WANG;School of Mathematics and Information Sciences,Henan University of Economics and Law;School of Mathematics Statistics, North China University of Water Resources and Electric Power;  
Let λ_1,λ_2,λ_3,λ_4 be non-zero real numbers, not all negative, and let λ_1/λ_2 be irrational and algebraic. Let ■ be a well-spaced sequence and δ 0. We prove that for any given ε 0, the number of v satisfying v ∈■ and v≤ X for which|λ_1 p_1~2+λ_2 p_2~2 + λ_3 p_3~3 +λ_4 p_4~3-v|v~(-δ) has no solution in primes p_1,p_2,p_3,p_4 does not exceed O(X~(7/8+2δ+ε)). This gives an improvement of an earlier result.
【Fund】: 国家自然科学基金资助项目(11371122 11471112);; 河南省科技创新杰出人才计划(134200510017);; 河南财经政法大学2016年青年拔尖人才
【CateGory Index】: O156.7
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【Citations】
Chinese Journal Full-text Database 3 Hits
1 MU Quanwu;LU Xiaodong;College of Science,Xi'an Polytechnic University;Department of Mathematics,Tongji University;;Diophantine Approximation with Prime Variables and Mixed Powers[J];数学年刊A辑(中文版);2015-03
2 Wei Ping LI Department of Mathematics and Information Science,Henan University of Economics and Law,Zhengzhou 450002,P.R.China Tian Ze WANG School of Mathematics and Information Science,North China University of Water Conservancy and Electric Power,Zhengzhou 450011,P.R.China;The Integral Part of a Nonlinear Form with k Powers of Primes[J];数学学报;2013-04
3 LI Weiping~1 WANG Tianze~2 1 Department of Mathematics and Information Science,Henan University of Finance and Economics,Zhengzhou 450002,China. 2 College of Mathematics and Information Science,North China Institute of Water Conservancy and Hydroelectric Power,Zhengzhou 450011,China.;Diophantine Approximation with Prime Variables and Mixed Powers[J];数学年刊A辑(中文版);2010-02
【Co-citations】
Chinese Journal Full-text Database 3 Hits
1 MU Quanwu;LU Xiaodong;College of Science,Xi'an Polytechnic University;Department of Mathematics,Tongji University;;Diophantine Approximation with Prime Variables and Mixed Powers[J];数学年刊A辑(中文版);2015-03
2 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.;Integral Part of a Nonlinear Form with Three Squares of Primes[J];数学年刊A辑(中文版);2011-06
3 Wei Ping LI Department of Mathematics and Information Science,Henan University of Economics and Law,Zhengzhou 450002,P.R.China Tian Ze WANG School of Mathematics and Information Science,North China University of Water Conservancy and Electric Power,Zhengzhou 450011,P.R.China;The Integral Part of a Nonlinear Form with Prime Variables[J];数学学报;2011-02
【Secondary Citations】
Chinese Journal Full-text Database 2 Hits
1 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.;Integral Part of a Nonlinear Form with Three Squares of Primes[J];数学年刊A辑(中文版);2011-06
2 LI Weiping~1 WANG Tianze~2 1 Department of Mathematics and Information Science,Henan University of Finance and Economics,Zhengzhou 450002,China. 2 College of Mathematics and Information Science,North China Institute of Water Conservancy and Hydroelectric Power,Zhengzhou 450011,China.;Diophantine Approximation with Prime Variables and Mixed Powers[J];数学年刊A辑(中文版);2010-02
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