Short‑Beam Chain‑Improvement for Li's Coefficients
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| Formato: | Recurso digital |
| Lenguaje: | inglés |
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2025
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| _version_ | 1866901685651111936 |
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| author | Kataoka, Hidetaro |
| author_facet | Kataoka, Hidetaro |
| contents | <p><span lang="EN-US">We prove, within an operator‑theoretic short‑beam chain‑improvement (SBCI) framework, the nonnegativity of Li‑type coefficients {λ_n}. The coefficients are realized as RKHS norms and as quadratic forms transported from a self‑adjoint model along a cyclic spectral bridge. A single L¹‑envelope controls all exchange operations; off‑real perimeter bounds give exponential‑moment control and Carleman determinacy. Uniform integrability (UIC–Carleson) and the Carleman condition are derived in‑body with constants depending only on the envelope and a fixed imaginary gap, hence independent of n. Combining these ingredients yields λ_n ≥ 0 for all n. Identification with the classical Li coefficients is optional and not used to prove positivity.</span></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17357554 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Short‑Beam Chain‑Improvement for Li's Coefficients Kataoka, Hidetaro Li coefficients, Riemann xi-function, reproducing-kernel Hilbert space, resolvent, Carleman, short-beam chain-improvement, spectral transfer <p><span lang="EN-US">We prove, within an operator‑theoretic short‑beam chain‑improvement (SBCI) framework, the nonnegativity of Li‑type coefficients {λ_n}. The coefficients are realized as RKHS norms and as quadratic forms transported from a self‑adjoint model along a cyclic spectral bridge. A single L¹‑envelope controls all exchange operations; off‑real perimeter bounds give exponential‑moment control and Carleman determinacy. Uniform integrability (UIC–Carleson) and the Carleman condition are derived in‑body with constants depending only on the envelope and a fixed imaginary gap, hence independent of n. Combining these ingredients yields λ_n ≥ 0 for all n. Identification with the classical Li coefficients is optional and not used to prove positivity.</span></p> |
| title | Short‑Beam Chain‑Improvement for Li's Coefficients |
| topic | Li coefficients, Riemann xi-function, reproducing-kernel Hilbert space, resolvent, Carleman, short-beam chain-improvement, spectral transfer |
| url | https://doi.org/10.5281/zenodo.17357554 |