A Proof of the Riemann Hypothesis

This paper presents an intuitive method for proving the Riemann Hypothesis. It begins by deriving the relationship equation at the zeros of the Riemann zeta function from Riemann's functional equation. This equation follows the Schwarz reflection principle, indicating that the zeros of the zeta function are restricted to the line with a real part of 1/2 in the complex plane. Furthermore, using the Schwarz reflection principle, it concludes that zeros cannot exist outside the critical line. Therefore, the Riemann Hypothesis is true.

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Publication Details

Journal
American Journal of Applied Mathematics and Statistics
Published
2024-12-04
DOI
https://doi.org/10.12691/ajams-12-4-3
Citations
3
Primary Topic
History and Theory of Mathematics
Type
article
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article

A Proof of the Riemann Hypothesis

Young Hwan Yun
3 citations
American Journal of Applied Mathematics and Statistics
History and Theory of Mathematics
article

A Proof of the Riemann Hypothesis

Young Hwan Yun
article en
3 citations

Abstract

This paper presents an intuitive method for proving the Riemann Hypothesis. It begins by deriving the relationship equation at the zeros of the Riemann zeta function from Riemann's functional equation. This equation follows the Schwarz reflection principle, indicating that the zeros of the zeta function are restricted to the line with a real part of 1/2 in the complex plane. Furthermore, using the Schwarz reflection principle, it concludes that zeros cannot exist outside the critical line. Therefore, the Riemann Hypothesis is true.

American Journal of Applied Mathematics and StatisticsVol. 12(4)
Openalex Percentile: Top 73%
History and Theory of Mathematics
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A Proof of the Riemann Hypothesis — Young Hwan Yun · American Journal of Applied Mathematics and Statistics (2024) | TGRS Research Map | TGRS