On the distribution of αp^2 + β modulo one for primes p such that p + 2 has no more two prime divisors

Abstract

A classical problem in analytic number theory is to study the distribution of frac- tional part αp^k + β, k ≥ 1 modulo 1, where α is irrational and p runs over the set of primes. We consider the subsequence generated by the primes p such that p + 2 is an almost-prime (the existence of infinitely many such p is another topical result in prime number theory) and prove that its distribution has a similar property.