Power spectrum of the fluctuation of Chebyshev's prime counting function

被引：1

作者：

Lan, BL ^{[1
]}

Yong, SJ ^{[1
]}

机构：

[1] Monash Univ, Sch Engn, Selangor 46150, Malaysia

来源：

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2006年 / 361卷 / 01期

关键词：

time series; fluctuation; Chebyshev's prime counting function; power-law power spectrum; Riemann hypothesis;

D O I：

10.1016/j.physa.2005.06.080

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The one-sided power spectrum of the fluctuation of Chebyshev's weighted prime counting function is numerically estimated based on samples of the fluctuating function of different sizes. The power spectrum is also estimated analytically for large frequency based on Riemann hypothesis and the exact formula for the fluctuating function in terms of all the non-trivial Riemann zeroes. Our analytical estimate is consistent with Our numerical estimate of a 1/f(2) power spectrum. (c) 2005 Elsevier B.V. All rights reserved.

引用

页码：35 / 40

页数：6

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