Multifractality of prime numbers

doi:10.1016/0378-4371(89)90461-5

Physica A: Statistical Mechanics and its Applications

Volume 160, Issue 1, 15 September 1989, Pages 24-42

https://doi.org/10.1016/0378-4371(89)90461-5 Get rights and content

Abstract

The multifractal formalism is applied to prime numbers. The spectrum of critical indices is found to be contained in the interval (α_min, 1), where α_min tends to 1 for increasing sets of numbers. Besides the scaling of moments with respect to the length of intervals the scaling with respect to the sizes of subsets of natural numbers is also considered. We have found the cusps in the plots of the functions $ƒ(α)$ and we claim that they are not caused by numerical roundings but they are a real effect. Besides the computer method, some analytical calculations are presented.

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Multifractality of prime numbers

Abstract

Phys. Rep.

Physics Today

Physica D

Phys. Rev. A

Phys. Rev. A

J. Phys. A

Phys. Rev. Lett.

Phys. Rev. Lett.

Phys. Rev. Lett.

Phys. Rev. A

Phys. Lett. A

Phys. Rev. A