Calculation of the Riemann Zeta-function on a Relativistic Computer
Mathematics and Computer Science
Volume 2, Issue 2, March 2017, Pages: 20-26
Received: May 10, 2017; Accepted: May 20, 2017; Published: Jul. 6, 2017
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Yuriy N. Zayko, Department of Applied Informatics, Faculty of Public Administration, The Russian Presidential Academy of National Economy and Public, Administration, Saratov Branch, Saratov, Russia
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The problem of calculating the sum of a divergent series for the Riemann ζ-function of a complex argument is considered in the paper, using the effects of the general theory of relativity. The parameters of the reference frame metric in which the calculation is performed are determined and solutions of the relativistic equations of motion of the material point realizing the calculation are found. 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. The formulation of the Riemann hypothesis concerning the distribution of nontrivial zeros of the ζ-function from the point of view of their computability on a relativistic computer is given. In view of the importance of the latter issue for studying the distribution of prime numbers, the results of the work may be of interest to specialists in the field of information security.
Metric, Riemann zeta-function, General Theory of Relativity, Space-Time Curvature, Non-computable Problems, Singularity, Black Hole, Relativistic Computer
To cite this article
Yuriy N. Zayko, Calculation of the Riemann Zeta-function on a Relativistic Computer, Mathematics and Computer Science. Vol. 2, No. 2, 2017, pp. 20-26. doi: 10.11648/j.mcs.20170202.12
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This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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