What question did this study set out to answer?

Determine improved lower bounds for the proportion of nontrivial zeros of the Riemann zeta function that are simple and lie on the critical line.

August 19, 2026Open Access

More than 79.47% of the zeros of the Riemann zeta function are simple and on the critical line

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Determine improved lower bounds for the proportion of nontrivial zeros of the Riemann zeta function that are simple and lie on the critical line.
Extended the Gabor-compressed Weil matrix framework to compute the third through sixth trace moments, proving the fourth moment exactly (m4 = 13/4).
Applied an exact Chebyshev–Markov dual certificate valid on unbounded support to bound zero proportions.
Machine-verified core algebraic identities, certificates, and pairing constants using Lean 4.
Proved that more than 79.47% of the nontrivial zeros of the Riemann zeta function are simple and lie on the critical line.
Established that more than 89.73% of the nontrivial zeros lie on the critical line.

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Implication

Theoretical proof reveals over 79.47% of Riemann zeta function zeros are simple and on the critical line, indicating significant progress toward the Riemann hypothesis.

Cite This Study

Hongyi et al. (2026) studied this question.

synapsesocial.com/papers/6a85639d03308d306e2d6d6d https://doi.org/10.5281/zenodo.21975237

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Implication

Theoretical proof reveals over 79.47% of Riemann zeta function zeros are simple and on the critical line, indicating significant progress toward the Riemann hypothesis.

More than 79.47% of the zeros of the Riemann zeta function are simple and on the critical line

Key Points

Discussion

Implication

Cite This Study

More than 79.47% of the zeros of the Riemann zeta function are simple and on the critical line

Key Points

Discussion

Implication

Cite This Study

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