Diophantine approximation by cobes of primes and an almost prime. II

摘要

Let λ1, ..., λ4 be non - zero with λ_1λ_2 irrational and nega - tive, and let S be the set of values attained by the form λ_1x~3_1+...+λ_4x~3_4 when x_1 has at most 3 prime divisors and the remaining variables are prime. We prove that most real numbers are close to an element of S.