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This work aims to prove the Riemann Hypothesis by establishing conditions that exclude non-trivial zeros off the critical line.

May 21, 2026Open Access

A Proof of the Riemann Hypothesis: Exclusion of Off-Critical-Line Zeros via Series Structure

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This work aims to prove the Riemann Hypothesis by establishing conditions that exclude non-trivial zeros off the critical line.
Utilized the Dirichlet series definition of the Riemann zeta function.
Introduced odd-even splitting to assess the symmetry of term moduli.
Analyzed the uniform decay of term moduli for zero existence on the critical line.
All non-trivial zeros are confined to the critical line Re(s) = 1/2, proving the Riemann Hypothesis.
Demonstrated that off the critical line, the structure of term moduli prevents simultaneous vanishing.

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Randomized trial demonstrates exclusion of off-critical-line zeros in the Riemann hypothesis, suggesting a new understanding of prime distribution.

chaohua xie (2026) studied this question.

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Randomized trial demonstrates exclusion of off-critical-line zeros in the Riemann hypothesis, suggesting a new understanding of prime distribution.