关于素变量的两个丢番图不等式(Ⅱ)  

On Two Diophantine Inequalities over Primes(Ⅱ)

作　　者：赵悦彤 李金蒋 张敏 ZHAO Yuetong;LI Jinjiang;ZHANG Min(School of Science,China University of Mining and Technology(Beijing),Beijing,100083,P.R.China;School of Applied Science,Beijing Information Science and Technology University,Beijing,100192,P.R.China)

机构地区：[1]中国矿业大学(北京)理学院,北京100083 [2]北京信息科技大学理学院,北京100192

出　　处：《数学进展》2023年第3期406-424,共19页Advances in Mathematics（China）

基　　金：Supported by NSFC(Nos.11901566,12001047,11971476,12071238);the Fundamental Research Funds for the Central Universities(No.2021YQLX02);the National Training Program of Innovation and Entrepreneurship for Undergraduates(No.202107010);the Undergraduate Education and Teaching Reform and Research Project for China University of Mining and Technology(Beijing)(No.J210703);the Scientific Research Funds of Beijing Information Science and Technology University(No.2025035)

摘　　要：设1<c<26088036/12301745,c≠2并且N为充分大的实数.本文证明了对于几乎所有的R∈(N,2N],丢番图不等式|p_(1)^(c)+p_(2)^(c)+p_(3)^(c)-R|<log^(-1)N关于素变量p1,p2,p3是可解的.进一步,我们证明了如下丢番图不等式|p_(1)^(c)+p_(2)^(c)+p_(3)^(c)+p_(4)^(c)+p_(5)^(c)+p_(6)^(c)-N|<log^(-1)N关于素变量p1,p2,p3,p4,p5,p6是可解的,改进了之前的结果1<c<37/18,c≠2.Let 1<c<26088036/12301745,c≠2 and N be a sufficiently large real number.In this paper,it is proved that,for almost all R∈(N,2N],the Diophantine inequality|p_(1)^(c)+p_(2)^(c)+p_(3)^(c)-R|<log^(-1)N is solvable in primes p1,p2,p3.Moreover,we also prove that the following Diophantine inequality|p_(1)^(c)+p_(2)^(c)+p_(3)^(c)+p_(4)^(c)+p_(5)^(c)+p_(6)^(c)-N|<log^(-1)N is solvable in prime variables p1,p2,p3,p4,p5,p6,which improves the previous result 1<c<37/18,c≠2.

关 键 词：丢番图不等式 素变量 指数和 

分 类 号：O156.4[理学—数学]