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.
出处
《纯粹数学与应用数学》
CSCD
北大核心
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).
关键词
算术数列
素变数
丢番图不等式
圆法
arithmetic progression, prime variables, diophantine inequality, circle method
