Diophantine Inequalities with Mixed Powers  

混合幂丢番图不等式（英文）

作　　者：牟全武 吕晓东 

机构地区：[1]College of Science, Xi'an Polytechnic University [2]Department of Mathematics, Tongji University

出　　处：《Chinese Quarterly Journal of Mathematics》2015年第4期545-554,共10页数学季刊（英文版）

基　　金：Supported by the National Natural Science Foundation of China(11201107,11271283,11501435);Supported by the Natural Science Foundation of Anhui Province(1208085QA01)

摘　　要：It is proved that if λ1,λ2,…,λ7 are nonzero real numbers, not all of the same sign and not all in rational ratios, then for any given real numbers η and σ, 0 〈 σ 〈 1/16, the inequality ｜λ1x1^2＋λ2x2^2＋∑i=3 7λixi^4＋η｜〈（max1≤i≤7｜xi｜-σhas infinitely many solutions in positive integers xl, x2,... , x7. Similax result is proved for ｜λ1x1^2＋λ2x2^2＋λ3x3^2＋λ4x4^4＋λ5x5^4＋λ6x6^4＋η｜〈（max1≤i≤7｜xi｜-σ.These results constitute an improvement upon those of Shi and Li.

关 键 词：diophantine inequality mixed power the Davenport-Heilbronn method 

分 类 号：O156.4[理学—数学]