The Proof of the Riemann Hypothesis on a Relativistic Turing Machine

Yuriy N. Zayko

doi:doi:10.11648/j.ijtam.20170306.17

| Peer-Reviewed

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

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

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), 2024. Published by Science Publishing Group

Keywords

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

References

[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.

Cite This Article

Plain Text BibTeX RIS

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

Copy | Download

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

Copy | Download

@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  -

Copy | Download

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

Download PDF

Sections

Plain Text BibTeX RIS

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

Copy | Download

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

Copy | Download

@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  -

Copy | Download