素变量混合幂丢番图逼近(Ⅱ)
Advances in Mathematics(China)（2017）
Abstract
设λ1,λ2,λ3,λ4是正实数,λ1/λ2是无理数和代数数,V是well-spaced序列,δ＞0.证明了:对于任意给定的大于或等于3的正整数k及任意ε＞0,v∈V,v≤X,使得|1λ1p1 + + λ4p4-v| ＜ v没有素数解p1,p2,p3,p4的v的个数不超过O(Xσ+2δ+ε),这里σ满足:当3≤k≤4时,σ=1-4/11k;当k≥5时,σ=σ =1-2/11k-16/11k2(k+1).这改进了之前[Chinese Ann.Math.Ser.A,2015,36(3):303-312]的结果.
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Key words
Diophantine inequalities,Davenport-Heilbronn method,prime
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