摘要
We investigate the exceptional set of real numbers not close to some value of a given binary linear form at prime arguments. Let λ1 and λ2 be positive real numbers such that λ1/λ2 is irrational and algebraic. For any （C, c） well-spaced sequence v and δ 〉 0, let E（v, X,δ ） denote the number of ν∈v with v ≤ X for which the inequality ｜λ1P1 ＋ λ2P2 - v｜ 〈 v-δ has no solution in primes P1,P2. It is shown that for any ε 〉 0, we have E（V, X, δ） 〈〈 max（X3/5＋2δ＋ε, X1/3＋4/3δ＋ε）.
We investigate the exceptional set of real numbers not close to some value of a given binary linear form at prime arguments. Let λ1 and λ2 be positive real numbers such that λ1/λ2 is irrational and algebraic. For any （C, c） well-spaced sequence v and δ 〉 0, let E（v, X,δ ） denote the number of ν∈v with v ≤ X for which the inequality ｜λ1P1 ＋ λ2P2 - v｜ 〈 v-δ has no solution in primes P1,P2. It is shown that for any ε 〉 0, we have E（V, X, δ） 〈〈 max（X3/5＋2δ＋ε, X1/3＋4/3δ＋ε）.
