Research Article
Open Access Peer-reviewed

A Proof of the Riemann Hypothesis

Young Hwan Yun
Zero Theoretical Physics Laboratory, Seoul, Republic of Korea
American Journal of Applied Mathematics and Statistics. 2024, 12(4), 86-92. DOI: 10.12691/ajams-12-4-3
Received October 25, 2024; Revised November 27, 2024; Accepted December 04, 2024

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.

Keywords:

Zeta function, nontrivial zeros, critical line, functional equation
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