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Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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Exact Certificates, Moment Ledgers, and a Three-Wall Barrier Map for Zero-Density Estimates at the Guth-Maynard Frontier

Authors: Güvenç, Güvenç;

Exact Certificates, Moment Ledgers, and a Three-Wall Barrier Map for Zero-Density Estimates at the Guth-Maynard Frontier

Abstract

We study the exponent-level structure of zero-density estimates for theRiemann zeta function around the Guth-Maynard bound A(sigma) = 4 route. Third, the extremal rational-concentration scenario is verified to be asimultaneous fixed point of four independent constraint families, includinga Rudin-Chang bound over the Q-dissociated log-prime system; a universalheight law B = T_1^(1/3) emerges across the whole range. Finally a single Alignment Hypothesis on linear-form correlations ofmollified Möbius coefficients is isolated and its exact price computed: ityields A(3/4) <= 420/191 but leaves the uniform exponent 30/13 invariant. All exponent arithmetic is verified in exact rational arithmetic. No newunconditional zero-density exponent is claimed; the contribution is thecertification of optimality for the stated inputs, the barrier map, and theconditional results. Verification code is available at the repository linkedbelow.

Keywords

additive energy, density hypothesis, Möbius correlations, analytic number theory, Riemann zeta function, large values of Dirichlet polynomials, zero-density estimates

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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