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American Journal of Applied Mathematics and Statistics. 2014, 2(2), 53-59
DOI: 10.12691/AJAMS-2-2-1
Original Research

Proof the Riemann Hypothesis

P.M. Mazurkin1,

1Doctor of Engineering Science, Academician of RANS, member of EANS, Volga Region State Technological University, Russia

Pub. Date: February 19, 2014
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Cite this paper

P.M. Mazurkin. Proof the Riemann Hypothesis. American Journal of Applied Mathematics and Statistics. 2014; 2(2):53-59. doi: 10.12691/AJAMS-2-2-1

Abstract

In the proof of the correctness of the Riemann hypothesis held strong Godel's incompleteness theorem. In keeping with the ideas of Poja and Hadamard's mathematical inventions, we decided to go beyond the modern achievements of the Gauss law of prime numbers and Riemann transformations in the complex numbers, knowing that at equipotent prime natural numbers will be sufficient mathematical transformations in real numbers. In simple numbers on the top left corner of the incidence matrix blocks are of the frame. When they move, a jump of the prime rate. Capacity of a number of prime numbers can be controlled by a frame, and they will be more reliable digits. In the column i=1 there is only one non-trivial zero on j=(0,∞). By the implicit Gaussian "normal" distribution , where Pj - a number of prime numbers with the order-rank j. On the critical line of the formula for prime numbers . By "the famous Riemann hypothesis is that the real part of the root is always exactly equal to 1/2" is obtained - the vibration frequency of a series of prime numbers is equal π/2, and the shift of the wave - π/4.

Keywords

prime numbers, the full range, critical line, the equation

Copyright

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References

[1]  Don Zagier. The first 50 million prime numbers. URL: http://www.ega-math.narod.ru/Liv/Zagier.htm.
 
[2]  Number. URL: http://ru.wikipedia.org/wiki/%D0%A7%D0%B8%D1%81%D0%BB%D0%BE.
 
[3]  Mazurkin P.M. Biotechnical principle and sustainable laws of distribution // Successes of modern natural sciences. 2009. № 9, 93-97.
 
[4]  Mazurkin PM The statistical model of the periodic system of chemical elements D.I. Mendeleev. Yoshkar-Ola: MarSTU, 2006. 152.