Volume 3, Issue 6, December 2017, Page: 219-224
The Proof of the Riemann Hypothesis on a Relativistic Turing Machine
Yuriy N. Zayko, Department of Applied Informatics, Faculty of Public Administration, The Russian Presidential Academy of National Economy and Public Administration, Saratov, Russia
Received: Oct. 2, 2017;       Accepted: Nov. 13, 2017;       Published: Jan. 2, 2018
DOI: 10.11648/j.ijtam.20170306.17      View  1591      Downloads  124
Abstract
In this article, the proof of the Riemann hypothesis is considered using the calculation of the Riemann ζ-function on a relativistic computer. The work lies at the junction of the direction known as "Beyond Turing", considering the application of the so-called "relativistic supercomputers" for solving non-computable problems and a direction devoted to the study of non-trivial zeros of the Riemann ζ-function. Considerations are given in favor of the validity of the Riemann hypothesis with respect to the distribution of non-trivial zeros of the ζ-function.
Keywords
Metric, Riemann ζ-Function, Non-Computable Problems, Singularity, Black Hole, Relativistic Computer, Riemann Hypothesis, Beyond Turing
To cite this article
Yuriy N. Zayko, The Proof of the Riemann Hypothesis on a Relativistic Turing Machine, International Journal of Theoretical and Applied Mathematics. Vol. 3, No. 6, 2017, pp. 219-224. doi: 10.11648/j.ijtam.20170306.17
Copyright
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Reference
[1]
Y. N. Zayko, Calculation of the Riemann Zeta-function on a Relativistic Computer, Mathematics and Computer Science, 2017; 2 (2): 20-26.
[2]
G. H. Hardy, Divergent Series, Oxford, 1949.
[3]
I. Nemeti, G. David, Relativistic Computers and the Turing Barrier. Applied Mathematics and Computation, 178, 118-142, 2006.
[4]
Y. N. Zayko, The Geometric Interpretation of Some Mathematical Expressions Containing the Riemann ζ-Function. Mathematics Letters, 2016; 2 (6): 42-46.
[5]
L. D. Landau, E. M. Lifshitz, The Classical Theory of Fields, (4th ed.), Butterworth-Heinemann, 1975.
[6]
L. G. Loitsyansky, Mechanics of Liquids and Gases, Moscow, Leningrad, GITTL, 1950 (Russian).
[7]
John Derbyshire, Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics, First Plume Printing, 2004.
[8]
Jinhua Fei, Riemann hypothesis is not correct, arXiv:1407. 4545v1 [math. GM] 17 Jul 2014.
[9]
A. Pr´astaro, The Riemann Hypothesis Proved, arXiv:1305. 6845v10 [math. GM] 27 Oct 2015.
[10]
R. C. McPhedran, Constructing a Proof of the Riemann Hypothesis, arXiv:1309. 5845v1 [math. NT] 30 Aug 2013.
[11]
Jin Gyu Lee, The Riemann Hypothesis and the possible proof, arXiv:1402. 2822v1 [math. GM] 9 Feb 2014.
[12]
V. Blinovsky, Proof of Riemann hypothesis, arXiv:1703. 03827v5 [math. GM] 1 May 2017.
[13]
F. Stenger, A Proof of the Riemann Hypothesis, arXiv:1708. 01209v2 [math. GM] 14 Aug 2017.
[14]
] M. Wolf, Will a physicist prove the Riemann Hypothesis?, arXiv:1410. 1214v3 [math-ph] 1 Dec 2015.
[15]
R. S. Mackay, Towards a Spectral Proof of Riemann's Hypothesis, arXiv:1708. 00440v1 [math. SP] 1 Aug 2017.
[16]
Yu. V. Matiyasevich, Alan Turing and Number Theory (to the 100 anniversary of A. Turing’s birth), The Alan Turing Centenary Conference (Manchester, UK, June 22–25 2012); Published in: Mathematics in Higher Education, 2012, № 10, 111-134 (Russian).
[17]
Y. N. Zayko, The Second Postulate of Euclid and the Hyperbolic Geometry, arXiv:1706. 08378.
[18]
Y. N. Zayko, Influence of Space-Time Curvature on the Light Propagation, SCIREA Journal of Physics, December 14, 2016, V. 1, № 1, 83-93.
[19]
Y. N. Zayko, The states in the band gap of a crystal localized in the region of inhomogeneity of the external field, Solid State Physics (SU), 1976. V. 18, № 4. P. 951-955.
[20]
E. O. Kane, Basic Ideas about Tunneling, in Tunneling Phenomena in Solids, Ed. by E. Burstein and S. Lundqvist, Plenum Press, NY, 1969.
Browse journals by subject