Primes in the form $[\alpha p+\beta]$
Number Theory
2008-04-05 v3
Abstract
Let \beta be a real number. Then for almost all irrational \alpha>0 (in the sense of Lebesgue measure) \limsup_{x\to\infty}\pi_{\alpha,\beta}^*(x)(\log x)^2/x>=1, where \pi_{\alpha,\beta}^*(x)={p<=x: both p and [\alpha p+\beta] are primes}.
Cite
@article{arxiv.0803.1740,
title = {Primes in the form $[\alpha p+\beta]$},
author = {Hongze Li and Hao Pan},
journal= {arXiv preprint arXiv:0803.1740},
year = {2008}
}