T. L. Todorova, D. I. Tolev
Published 2007-11-01, updated 2007-11-07Version 2
A classical problem in analytic number theory is to study the distribution of $\alpha p$ modulo 1, where $\alpha$ 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.
On the distribution of $αp+β$ modulo one for primes of type $p=ar^2+1$
On the distribution of $αp^2+β$ modulo one for primes $p$ such that $p+2$ has no more two prime divisors
Estimates of the bounds of $π(x)$ and $π((x+1)^{2}-x^{2})$
![QR code for arXiv:0711.0171 [math.NT]](http://oss.arxitics.com/images/favicon.svg)