English

On the distribution of $\alpha p+\beta$ modulo one for primes of type $p=ar^2+1$

Number Theory 2024-04-05 v2

Abstract

A classical problem in analytic number theory is to study the distribution of fractional part αp+β\alpha p+\beta modulo 1, where α\alpha is irrational and pp runs over the set of primes. We consider the subsequence generated by the primes pp such that p=ar2+1p=ar^2+1 and prove that its distribution has a similar property.

Keywords

Cite

@article{arxiv.2404.01047,
  title  = {On the distribution of $\alpha p+\beta$ modulo one for primes of type $p=ar^2+1$},
  author = {T. Todorova},
  journal= {arXiv preprint arXiv:2404.01047},
  year   = {2024}
}