Independent Research, 2026
We present a rigorous derivation of the Riemann Hypothesis (RH) by constructing a global structur... more We present a rigorous derivation of the Riemann Hypothesis (RH) by constructing a global structural operator Hsa on a weighted Hilbert space Hw. By defining a structural index B(s) invariant under the functional equation s → 1-s, we establish a correspondence between the non-trivial zeros of the Riemann zeta function ζ(s) and the spectrum of Hsa. Utilizing the Guinand-Weil explicit formula and a trace-class regularization, we prove that the spectral trace of this operator is strictly positive if any zero lies off the critical line. However, the global functional symmetry of ζ(s) enforces the vanishing of the trace on the quotient space of the functional equation. This contradiction forces the "spectral deviation" terms (β-1/2) 2 to vanish individually. Consequently, all non-trivial zeros satisfy ℜ(s) = 1/2. We provide a technical appendix detailing the analytic bounds, kernel decay, and pole regularization to ensure the operator is well-defined.
"This paper is archived and indexed on Zenodo with [DOI: 10.5281/zenodo.18644228]".
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Papers by Ahmed Benadiel
"This paper is archived and indexed on Zenodo with [DOI: 10.5281/zenodo.18644228]".