素变量混合幂丢番图逼近  

Diophantine Approximation with Prime Variables and Mixed Powers

作　　者：李伟平 戈文旭[2] 王天泽[2] Wei Ping LI;Wen Xu GE;Tian Ze WANG(School of Mathematics and Information Sciences,Henan University of Economics and Law,Zhengzhou 450046,P.R.China;School of Mathematics Statistics,North China University of Water Resources and Electric Power,Zhengzhou 450046,P.R.China)

机构地区：[1]河南财经政法大学数学与信息科学学院,郑州450046 [2]华北水利水电大学数学与统计科学学院,郑州450046

出　　处：《数学学报（中文版）》2019年第1期49-58,共10页Acta Mathematica Sinica：Chinese Series

基　　金：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

摘　　要：设λ_1,λ_2,λ_3,λ_4为不全为负的非零实数,λ_1/λ_2是无理数和代数数.■是具有良好间隔的序列,δ>0.本文证明了:对于任意ε>0及v∈■,v≤X,使得不等式|λ_1p_1~2+λ_2p_2~2+λ_3p_3~3+λ_4p_4~3-v|<v^(-δ)无素数解p_1,p_2,p_3,p_4的v的个数不超过O(X^(7/8+2δ+ε)).这改进了之前的结果.Let λ1,λ2,λ3,λ4 be non-zero real numbers, not all negative, and let λ1/λ2 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|λ1 p12+λ2 p22 + λ3 p33 +λ4 p43-v|<v-δ has no solution in primes p1,p2,p3,p4 does not exceed O(X7/8+2δ+ε). This gives an improvement of an earlier result.

关 键 词：丢番图不等式 素数 Davenport-Heilbronn方法 

分 类 号：O156.4[理学—数学]