The Geometric Interpretation of Some Mathematical Expressions Containing the Riemann ζ-Function
Mathematics Letters
Volume 2, Issue 6, December 2016, Pages: 42-46
Received: Oct. 6, 2016; Accepted: Nov. 10, 2016; Published: Dec. 17, 2016
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Author
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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Abstract
The article discusses some of the mathematical results widely used in practice which contain the Riemann ζ-function, and, at first glance, are in contradiction with common sense. A geometric approach is suggested, based on the concept of the curvature of space, in which is calculated an algorithm that specifies the representation of ζ-function as an infinite diverging series. The analysis is based on the use of Einstein equations to calculate the metric of curved space-time. The solution of the Einstein equations is a metric that has a singularity, like the metric in the vicinity of the black hole. The result can be interpreted in the spirit of a Turing machine that performs the proposed algorithm for calculating the sum of a divergent series.
Keywords
Riemann ζ-Function, Einstein Equations, Metric, Metric Tensor, Energy-Momentum Tensor, Christoffel Symbols, Algorithm, Turing Machine
To cite this article
Yuriy N. Zayko, The Geometric Interpretation of Some Mathematical Expressions Containing the Riemann ζ-Function, Mathematics Letters. Vol. 2, No. 6, 2016, pp. 42-46. doi: 10.11648/j.ml.20160206.11
Copyright
Copyright © 2016 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.
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