| _version_ | 1866902087126745088 |
|---|---|
| author | Fradkin, Yuval |
| author_facet | Fradkin, Yuval |
| contents | <div> <div> <div> <div dir="auto"> <div> <div> <p>We develop a symmetry-based analytic approach to the Riemann Hypothesis that couples dyadic (base-2) “row” symmetry with quantitative boundary approximation on narrow rectangles around the critical line. The framework introduces smoothed, exactly symmetric Dirichlet filters and represents</p> F(s)=(−ζ′ζ)(s) G(s)F(s)=\Bigl(-\frac{\zeta'}{\zeta}\Bigr)(s)\,G(s)F(s)=(−ζζ′)(s)G(s) <p>so that zeros of ζ\zetaζ are detected without artificial cancellation. Using Abel summation, explicit-formula identities, Littlewood’s rectangle lemma, Poisson–Jensen, and three-lines propagation, we convert small symmetric boundary error for FFF into interior zero localization and global O(logT)O(\log T)O(logT) control of weighted zero sums. A height-adaptive construction yields uniform boundary approximants to (−ζ′/ζ)−1(-\zeta'/\zeta)^{-1}(−ζ′/ζ)−1 with calibrated accuracy and polynomial complexity, enforcing near-unity on the boundary and excluding off-critical zeros in the interior under mild strip bounds. The result is a clear, testable linkage between symmetric boundary approximation and critical-line zero concentration, with constants tracked for rigorous scrutiny.</p> </div> </div> </div> </div> <div> </div> <div> <div> </div> </div> </div> </div> <div> </div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17208227 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Symmetry-Based Boundary Approximation and Zero Localization for the Riemann Zeta Function Fradkin, Yuval <div> <div> <div> <div dir="auto"> <div> <div> <p>We develop a symmetry-based analytic approach to the Riemann Hypothesis that couples dyadic (base-2) “row” symmetry with quantitative boundary approximation on narrow rectangles around the critical line. The framework introduces smoothed, exactly symmetric Dirichlet filters and represents</p> F(s)=(−ζ′ζ)(s) G(s)F(s)=\Bigl(-\frac{\zeta'}{\zeta}\Bigr)(s)\,G(s)F(s)=(−ζζ′)(s)G(s) <p>so that zeros of ζ\zetaζ are detected without artificial cancellation. Using Abel summation, explicit-formula identities, Littlewood’s rectangle lemma, Poisson–Jensen, and three-lines propagation, we convert small symmetric boundary error for FFF into interior zero localization and global O(logT)O(\log T)O(logT) control of weighted zero sums. A height-adaptive construction yields uniform boundary approximants to (−ζ′/ζ)−1(-\zeta'/\zeta)^{-1}(−ζ′/ζ)−1 with calibrated accuracy and polynomial complexity, enforcing near-unity on the boundary and excluding off-critical zeros in the interior under mild strip bounds. The result is a clear, testable linkage between symmetric boundary approximation and critical-line zero concentration, with constants tracked for rigorous scrutiny.</p> </div> </div> </div> </div> <div> </div> <div> <div> </div> </div> </div> </div> <div> </div> |
| title | Symmetry-Based Boundary Approximation and Zero Localization for the Riemann Zeta Function |
| url | https://doi.org/10.5281/zenodo.17208227 |