What does this research mean for the field?

All non-trivial zeros of the Riemann zeta function have a real part of exactly 1/2, thus proving the Riemann Hypothesis. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.CHALLENGES_CONSENSUS.

What question did this study set out to answer?

The aim is to provide proof of the Riemann Hypothesis by exploring properties of the Dirichlet eta function.

February 16, 2026Open Access

On the Constant Real Part of Non-Trivial Zeros: A Proof of the Riemann Hypothesis

Puntos clave

The aim is to provide proof of the Riemann Hypothesis by exploring properties of the Dirichlet eta function.
Examining the geometric and arithmetic properties of the Dirichlet eta function
Assuming zeros exist off the critical line
Analyzing the resulting alternating series in the complex plane
Establishing a logical contradiction with assumed zeros off the critical line
Demonstrating all non-trivial zeros must have a real part of 1/2

Resumen

This paper presents a proof of the Riemann Hypothesis by examining the geometric and arithmetic properties of the Dirichlet eta function. By assuming the existence of zeros off the critical line, and analyzing the resulting alternating series in the complex plane, we establish a logical contradiction. The proof relies on insights into the structure of these series, demonstrating that all non-trivial zeros must possess a real part of exactly 1/2.

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