Scale invariant correlations and the distribution of prime numbers

Details Scale invariant correlations and the distribution of prime numbers Scale invariant correlations and the distribution of prime numbers

2009-03-16

arxiv.org/abs/0903.2592v3

J. Phys. A: Math. Theor. 42 345102 (2009)

Physics

Mathematical Physics

13 pages, 8 figures, version to appear in J. Phys. A

Scientific paper

10.1088/1751-8113/42/34/345102

Negative correlations in the distribution of prime numbers are found to display a scale invariance. This occurs in conjunction with a nonstationary behavior. We compare the prime number series to a type of fractional Brownian motion which incorporates both the scale invariance and the nonstationary behavior. Interesting discrepancies remain. The scale invariance also appears to imply the Riemann hypothesis and we study the use of the former as a test of the latter.

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