Primes in short intervals

Details Primes in short intervals Primes in short intervals

2004-09-15

arxiv.org/abs/math/0409258v1

Mathematics

Number Theory

29 pages

Scientific paper

10.1007/s00220-004-1222-4

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 $\psi(x+H)- \psi(x)$, for $0\le x\le N$, is approximately
normal with mean $\sim H$ and variance $\sim H\log N/H$, when $N^\delta \le H
\le N^{1-\delta}$.

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