| _version_ | 1866901396914176000 |
|---|---|
| author | Karadzhov, Tosho Lazarov |
| author_facet | Karadzhov, Tosho Lazarov |
| contents | <p>This module discharges the TP-specific assumptions from the TEBAC HP corpus (T1 arithmetic circle action/invariance, T3 end-translation model for prime correspondences, and T5 semigroupoid closure). It provides a justified trace--prime conversion on real $s>1$, producing an error term that extends holomorphically to the wedge \[ \mathfrak W_c \;=\; \bigl\{\,s\in\mathbb C : \Re\bigl((s-\tfrac12)^2\bigr) > -c \bigr\}, \] with all Tonelli/Fubini interchanges proved at module level. A key analytic ingredient is a self-contained Gaussian heat-kernel upper bound for the explicit HP--II end operator \[ -\partial_u^2 + \alpha e^{2u} + \beta e^{-2u} + R(u), \] proved via truncation and Trotter domination and re-derived via a Brownian-bridge (Feynman--Kac) representation in the appendix. This preprint is part of the TEBAC Hilbert--Pólya program.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18843073 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | TEBAC HP III: The GL(1) Trace–Prime Package (TP), Fully Discharged Karadzhov, Tosho Lazarov TEBAC; Hilbert–Pólya; Riemann hypothesis; trace formula; GL(1); heat kernel; zeta determinant; Laplace transform; prime powers; spectral theory; noncommutative geometry; explicit formula <p>This module discharges the TP-specific assumptions from the TEBAC HP corpus (T1 arithmetic circle action/invariance, T3 end-translation model for prime correspondences, and T5 semigroupoid closure). It provides a justified trace--prime conversion on real $s>1$, producing an error term that extends holomorphically to the wedge \[ \mathfrak W_c \;=\; \bigl\{\,s\in\mathbb C : \Re\bigl((s-\tfrac12)^2\bigr) > -c \bigr\}, \] with all Tonelli/Fubini interchanges proved at module level. A key analytic ingredient is a self-contained Gaussian heat-kernel upper bound for the explicit HP--II end operator \[ -\partial_u^2 + \alpha e^{2u} + \beta e^{-2u} + R(u), \] proved via truncation and Trotter domination and re-derived via a Brownian-bridge (Feynman--Kac) representation in the appendix. This preprint is part of the TEBAC Hilbert--Pólya program.</p> |
| title | TEBAC HP III: The GL(1) Trace–Prime Package (TP), Fully Discharged |
| topic | TEBAC; Hilbert–Pólya; Riemann hypothesis; trace formula; GL(1); heat kernel; zeta determinant; Laplace transform; prime powers; spectral theory; noncommutative geometry; explicit formula |
| url | https://doi.org/10.5281/zenodo.18843073 |