Diophantine approximation by special primes

Abstract

We show that whenever $\delta >0$, $\eta$ is real and constants ${\lambda }_i$ satisfy some necessary conditions, there are infinitely many prime triples $p_1,p_2,p_3$ satisfying the inequality $|{\lambda }_1{p}_1+{\lambda }_2{p}_2+{\lambda }_3{p}_3+\eta |<(\max p_j{)}^{-1/12+\delta }$ and such that, for each $i\in \{1,2,3\}$, $p_i+2$ has at most $28$ prime factors.

References in corpus (1)

• Vinogradov's three primes theorem with almost twin primes