A Proof of the Riemann Hypothesis
A Proof of the Riemann Hypothesis By Iakovos Koukas (April 2024) Abstract: The Riemann Hypothesis, proposed by Bernhard Riemann in 1859, remains one of the most profound unsolved conjectures in mathematics. This paper presents a comprehensive proof of the Riemann Hypothesis, through eight steps that use mathematical tools from complex analysis, number theory, and mathematical logic. Beginning with the foundational definition of the Riemann zeta function, I extend its domain analytically, investigate its behavior within the critical strip, and use various mathematical techniques to establish the distribution of its non-trivial zeros. Through analytical reasoning and careful application of mathematical principles, I demonstrate that all non-trivial zeros of the Riemann zeta function lie on the critical line, thereby proving the Riemann Hypothesis. Introduction: The Riemann Hypothesis is a conjecture concerning the non-trivial zeros of the Riemann zeta function, a central object in