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Detection and Discrimination of the Periodicity of Prime Numbers by Discrete Fourier Transform – Symphony of Primes

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Title: Detection and Discrimination of the Periodicity of Prime Numbers by Discrete Fourier Transform – Symphony of Primes

Authors: L. Csoka

Journal: Journal of advances in applied & computational mathematics

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Year: 2015

Volume: 2

Issue: 1

Language: en

DOI: 10.15377/2409-5761.2014.02.01.1

Keywords: discrete Fourier transformVon Mangoldt functionprime numbers.

Categories
Signal Processing (1285) Fourier Analysis (7) Prime Numbers (1) Number Theory (108) Mathematics (5170)

Abstract

A novel representation of a quasi-periodic modified von Mangoldt function L(n) on prime numbers and its decomposition into Fourier series has been investigated. We focus on some particular quantities characterizing the modified von Mangoldt function. The results indicate that prime number progression can be decomposed into periodic sequences. The main approach is to decompose it into sin or cosine function. Basically, it is applied to extract hidden periodicities in seemingly quasi periodic prime function. Numerical evidences were provided to confirm the periodic distribution of primes.

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