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Communications in Mathematical Physics

, Volume 252, Issue 1–3, pp 589–617 | Cite as

Primes in Short Intervals

  • Hugh L. MontgomeryEmail author
  • K. Soundararajan
Article

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≤xN, is approximately normal with mean ∼H and variance ∼H log N/H, when N δ HN1− δ .

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Short Interval 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA

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