Distribution of αp2 Modulo One with Prime Variable p of a Special Form - Fei Xue; Jinjiang Li; Min Zhang (Journal of Mathematics)
Let Pr denote an almost-prime with at most r prime factors, counted according to multiplicity. In this paper, it is proved that, for α∈ℝ/ℚ, β∈ℝ, and 0<θ<10/1561, there exist infinitely many primes p, such that αp2+β<p−θ and p+2=P4, which constitutes an improvement upon the previous result.