算术数列中的素变数丢番图逼近  

Diophantine approximation by prime varibles in arithmetic progressions

作　　者：李伟平[1] 

机构地区：[1]同济大学应用数学系

出　　处：《纯粹数学与应用数学》2005年第1期1-4,10,共5页Pure and Applied Mathematics

基　　金：国家自然科学基金项目资助(10171076);上海市科委基金项目资助(03JC14027).

摘　　要：证明了:设λ1,λ2,λ3是非零实数,并且不同一符号,η是实数,λ1/λ2是无理数,h是一个给定的正整数,l1,l2,l3是整数,如果广义黎曼猜想成立,那么有无穷多有序素数对p1,p2,p3(pj≡lj(modh),j=1,2,3)使得|λ1p1+λ2p2+λ3p3+η|<(maxpj)-110(logmaxpj)5.In this paper, it is proved: suppose that λ_1,λ_2,λ_3 are nonzero real numbers not all of the same sign, that η is real, λ_1/λ_2 is irrational, that h is a given positive integer, l_1,l_2,l_3 are integers, and that GRH is correct, then there are infinitely many ordered triples p_1,p_2,p_3 (p_j≡l_j(mod h),j=1,2,3) such that ｜λ_1p_1+λ_2p_2+λ_3p_3+η｜<(max p_j)^(-110)(log max p_j)~5.

关 键 词：算术数列 素变数 丢番图不等式 圆法 

分 类 号：O156.4[理学—数学]