摘要
证明了:如果λ_1,λ_2,λ_3,λ_4是正实数,λ_1/λ_2是无理数和代数数,V是well-spaced序列,δ>0,那么对于v∈V,v≤X,ε>0,使得|λ_(1p_1~2)+λ_(2p_2~2)+λ_(3p_3~3)+λ_(4p_4~3)-v|<v^(-δ)没有素数解p1,p2,p3,p4的v的个数不超过O(X^(20/21+21δ+ε)).
This paper shows that： Let λ1,λ2,λ3,λ4 be positive real numbers and suppose that λ1/λ2 is irrational and algebraic. Let V be a well-spaced sequence, δ 〉 0. Then, for any given ε 〉 0, the number of v ∈ V with v ∈ X for which ｜λ1p1^2＋λ2p2^2＋λ4p4^3-v｜〈v-δ has no solution in primes Pl, P2, P3, P4 does not exceed O（x^20/21＋2δ＋ε）
出处
《数学年刊（A辑）》
CSCD
北大核心
2010年第2期247-256,共10页
Chinese Annals of Mathematics
基金
国家自然科学基金(No.10671056)资助的项目
