Power spectrum of the difference between the prime-number counting function and Riemann's function: 1/f2?

Boon Leong Lan and Shaohen Yong

Physica A: Statistical Mechanics and its Applications, 2004, vol. 334, issue 3, 477-481

Abstract: Gamba et al. [Phys. Lett. A 145 (1990) 106] numerically estimated the power spectrum of the difference between the prime-number counting function π(x) and its approximate given by Riemann's function R(x), but did not determine the functional dependence of the spectrum on the frequency. Our numerical estimates, based on samples of the difference function R(x)−π(x) at integer x up to x=109, strongly suggest that the difference function has a 1/f2 power spectrum.

Keywords: Time series; Prime counting function; Riemann's function; Power-law power spectrum (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:334:y:2004:i:3:p:477-481

DOI: 10.1016/j.physa.2003.10.015

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