Explicit Isolation Bounds for Zeta Zeros at Fixed Small Spacings: Signed Complex-Block Allocation and a Certified Fourier Test

This independent preprint develops a complex finite-multiset inequality using signed Hilbert-space blocks and a deterministic allocation of screening centers. Coupled with unconditional fixed-test weighted pair correlation, Conrey's integrated off-line zero-density estimate, and strict computer-assisted Fourier interval certificates for an explicitly smoothed forty-mode density, the method yields proposed quantitative isolation bounds for zeta zeros at two fixed locally normalized spacings: more than 0.655208 at c=0.00575 and more than 0.655200 at c=0.005966. A sharp real-supported forest inequality identifies a simpler benchmark. The signed decomposition itself is not claimed as new over Lamzouri. The new complex blocking and numerical package await external specialist verification; this preprint does not prove RH/GRH or any positive lower density of non-isolated zeros.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-28
DOI
https://doi.org/10.5281/zenodo.23719901
Primary Topic
Analytic Number Theory Research
Type
preprint
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preprint

Explicit Isolation Bounds for Zeta Zeros at Fixed Small Spacings: Signed Complex-Block Allocation and a Certified Fourier Test

Byoungwoo Lee
5 links
Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
preprint

Explicit Isolation Bounds for Zeta Zeros at Fixed Small Spacings: Signed Complex-Block Allocation and a Certified Fourier Test

Byoungwoo Lee
preprint en

Abstract

This independent preprint develops a complex finite-multiset inequality using signed Hilbert-space blocks and a deterministic allocation of screening centers. Coupled with unconditional fixed-test weighted pair correlation, Conrey's integrated off-line zero-density estimate, and strict computer-assisted Fourier interval certificates for an explicitly smoothed forty-mode density, the method yields proposed quantitative isolation bounds for zeta zeros at two fixed locally normalized spacings: more than 0.655208 at c=0.00575 and more than 0.655200 at c=0.005966. A sharp real-supported forest inequality identifies a simpler benchmark. The signed decomposition itself is not claimed as new over Lamzouri. The new complex blocking and numerical package await external specialist verification; this preprint does not prove RH/GRH or any positive lower density of non-isolated zeros.

Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
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