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"Riemann-Schwarz principle", Encyclopedia of Mathematics, EMS Press, 2001 [1994].

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Article

A Proof of the Riemann Hypothesis

1Zero Theoretical Physics Laboratory, Seoul, Republic of Korea


American Journal of Applied Mathematics and Statistics. 2024, Vol. 12 No. 4, 86-92
DOI: 10.12691/ajams-12-4-3
Copyright © 2024 Science and Education Publishing

Cite this paper:
Young Hwan Yun. A Proof of the Riemann Hypothesis. American Journal of Applied Mathematics and Statistics. 2024; 12(4):86-92. doi: 10.12691/ajams-12-4-3.

Correspondence to: Young  Hwan Yun, Zero Theoretical Physics Laboratory, Seoul, Republic of Korea. Email: yhyun690@naver.com, younghwan.yun@snu.ac.kr

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.

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