Primes in short intervals
Hugh L. Montgomery, K. Soundararajan
Abstract
Contrary to what would be predicted on the basis of Cramér's model concerning the distribution of prime numbers, we develop evidence that the distribution of ψ(x+H)- ψ(x), for 0 x N, is approximately normal with mean H and variance H N/H, when Nδ H N1-δ.
Create a lesson
Related papers
An ergodic approach to equations of the form x+y=α(n)
Vitaly Bergelson, Hao Pan, Saúl Rodríguez Martín
Rogers--Ramanujan identities from the geometry of Xa=Yb
Yifeng Huang, Kenny Lau, Ken Ono
Computational results on sums of a prime with squares or cubes
Kenny Applegate, Kyle Pratt
Finding New Limit Points of Mahler Measure by Methods of Missing Data Restoration
Jean-Marc Sac-Épée, Souad El Otmani, Armand Maul et al.
Low moments of automorphic random multiplicative function sums
Sun-Kai Leung
A problem of Yang and Chen on weighted representation functions
Shuang-Shuang Li, Ya-Ting Xu, Xiao-Hui Yan