English

Primes in short intervals

Number Theory 2009-11-10 v1

Abstract

Contrary to what would be predicted on the basis of Cram\'er's model concerning the distribution of prime numbers, we develop evidence that the distribution of ψ(x+H)ψ(x)\psi(x+H)- \psi(x), for 0xN0\le x\le N, is approximately normal with mean H\sim H and variance HlogN/H\sim H\log N/H, when NδHN1δN^\delta \le H \le N^{1-\delta}.

Keywords

Cite

@article{arxiv.math/0409258,
  title  = {Primes in short intervals},
  author = {Hugh L. Montgomery and K. Soundararajan},
  journal= {arXiv preprint arXiv:math/0409258},
  year   = {2009}
}

Comments

29 pages