The Proof of the Riemann Hypothesis on a Relativistic Turing Machine

Yuriy N. Zayko

doi:doi:10.11648/j.ijtam.20170306.17

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The Proof of the Riemann Hypothesis on a Relativistic Turing Machine

Yuriy N. Zayko

Published in International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 6)

Received: 2 October 2017 Accepted: 13 November 2017 Published: 2 January 2018

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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.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 6)
DOI	10.11648/j.ijtam.20170306.17
Page(s)	219-224
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

Metric, Riemann ζ-Function, Non-Computable Problems, Singularity, Black Hole, Relativistic Computer, Riemann Hypothesis, Beyond Turing

References

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[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).
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[20]	E. O. Kane, Basic Ideas about Tunneling, in Tunneling Phenomena in Solids, Ed. by E. Burstein and S. Lundqvist, Plenum Press, NY, 1969.

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Yuriy N. Zayko. (2018). The Proof of the Riemann Hypothesis on a Relativistic Turing Machine. International Journal of Theoretical and Applied Mathematics, 3(6), 219-224. https://doi.org/10.11648/j.ijtam.20170306.17

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ACS Style

Yuriy N. Zayko. The Proof of the Riemann Hypothesis on a Relativistic Turing Machine. Int. J. Theor. Appl. Math. 2018, 3(6), 219-224. doi: 10.11648/j.ijtam.20170306.17

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AMA Style

Yuriy N. Zayko. The Proof of the Riemann Hypothesis on a Relativistic Turing Machine. Int J Theor Appl Math. 2018;3(6):219-224. doi: 10.11648/j.ijtam.20170306.17

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@article{10.11648/j.ijtam.20170306.17,
  author = {Yuriy N. Zayko},
  title = {The Proof of the Riemann Hypothesis on a Relativistic Turing Machine},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {3},
  number = {6},
  pages = {219-224},
  doi = {10.11648/j.ijtam.20170306.17},
  url = {https://doi.org/10.11648/j.ijtam.20170306.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20170306.17},
  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.},
 year = {2018}
}

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TY  - JOUR
T1  - The Proof of the Riemann Hypothesis on a Relativistic Turing Machine
AU  - Yuriy N. Zayko
Y1  - 2018/01/02
PY  - 2018
N1  - https://doi.org/10.11648/j.ijtam.20170306.17
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T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 219
EP  - 224
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20170306.17
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Author Information

Yuriy N. Zayko

Department of Applied Informatics, Faculty of Public Administration, The Russian Presidential Academy of National Economy and Public Administration, Saratov, Russia

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APA Style

Yuriy N. Zayko. (2018). The Proof of the Riemann Hypothesis on a Relativistic Turing Machine. International Journal of Theoretical and Applied Mathematics, 3(6), 219-224. https://doi.org/10.11648/j.ijtam.20170306.17

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ACS Style

Yuriy N. Zayko. The Proof of the Riemann Hypothesis on a Relativistic Turing Machine. Int. J. Theor. Appl. Math. 2018, 3(6), 219-224. doi: 10.11648/j.ijtam.20170306.17

Copy | Download

AMA Style

Yuriy N. Zayko. The Proof of the Riemann Hypothesis on a Relativistic Turing Machine. Int J Theor Appl Math. 2018;3(6):219-224. doi: 10.11648/j.ijtam.20170306.17

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@article{10.11648/j.ijtam.20170306.17,
  author = {Yuriy N. Zayko},
  title = {The Proof of the Riemann Hypothesis on a Relativistic Turing Machine},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {3},
  number = {6},
  pages = {219-224},
  doi = {10.11648/j.ijtam.20170306.17},
  url = {https://doi.org/10.11648/j.ijtam.20170306.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20170306.17},
  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.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - The Proof of the Riemann Hypothesis on a Relativistic Turing Machine
AU  - Yuriy N. Zayko
Y1  - 2018/01/02
PY  - 2018
N1  - https://doi.org/10.11648/j.ijtam.20170306.17
DO  - 10.11648/j.ijtam.20170306.17
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 219
EP  - 224
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20170306.17
AB  - 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.
VL  - 3
IS  - 6
ER  -

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