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.
| Published in | Mathematics Letters (Volume 2, Issue 6) |
| DOI | 10.11648/j.ml.20160206.11 |
| Page(s) | 42-46 |
| 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), 2016. Published by Science Publishing Group |
Riemann ζ-Function, Einstein Equations, Metric, Metric Tensor, Energy-Momentum Tensor, Christoffel Symbols, Algorithm, Turing Machine
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APA Style
Yuriy N. Zayko. (2016). The Geometric Interpretation of Some Mathematical Expressions Containing the Riemann ζ-Function. Mathematics Letters, 2(6), 42-46. https://doi.org/10.11648/j.ml.20160206.11
ACS Style
Yuriy N. Zayko. The Geometric Interpretation of Some Mathematical Expressions Containing the Riemann ζ-Function. Math. Lett. 2016, 2(6), 42-46. doi: 10.11648/j.ml.20160206.11
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Download@article{10.11648/j.ml.20160206.11,
author = {Yuriy N. Zayko},
title = {The Geometric Interpretation of Some Mathematical Expressions Containing the Riemann ζ-Function},
journal = {Mathematics Letters},
volume = {2},
number = {6},
pages = {42-46},
doi = {10.11648/j.ml.20160206.11},
url = {https://doi.org/10.11648/j.ml.20160206.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ml.20160206.11},
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.},
year = {2016}
}
TY - JOUR T1 - The Geometric Interpretation of Some Mathematical Expressions Containing the Riemann ζ-Function AU - Yuriy N. Zayko Y1 - 2016/12/17 PY - 2016 N1 - https://doi.org/10.11648/j.ml.20160206.11 DO - 10.11648/j.ml.20160206.11 T2 - Mathematics Letters JF - Mathematics Letters JO - Mathematics Letters SP - 42 EP - 46 PB - Science Publishing Group SN - 2575-5056 UR - https://doi.org/10.11648/j.ml.20160206.11 AB - 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. VL - 2 IS - 6 ER -
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