Riemann Hypothesis Papers
Research publications on the Riemann zeta function, Weil explicit formula, spectral approaches, and the Weil–Connes programme by Kerym Makraini.
UNED National University of Distance Education, Madrid, Spain
AGE Quantum Gates Engine S.L., Melilla, Spain
Spectral Properties of the Truncated Weil Operator & Numerical Verification of Weil Positivity
Kerym Makraini
We study the truncated Weil operator A_Λ on L²([-log Λ, log Λ]), following Connes's programme for the Riemann Hypothesis. We establish spectral properties and provide numerical verification of Weil positivity conditions. The paper introduces rigorous numerical methods for verifying the Weil positivity condition essential to Connes's approach to the Riemann Hypothesis.
Spectral Detection of Automorphic & Arithmetic Zeros: Mayer–Ruelle Verification, Eisenstein Scattering, & Negative Diagnostics
Kerym Makraini
Our methodological principle is that an operator construction for zeros of L-functions should be accepted only when it is anchored to a rigid mathematical identity—a theorem, not a numerical coincidence. We develop rigorous criteria for distinguishing true spectral origins of zeros from mere numerical correlations. The work applies Mayer–Ruelle scattering theory to identify genuine automorphic contributions.
Spectral Persistence and Kreĭin Rigidity in the Weil–Connes Programme
Kerym Makraini
We develop a conditional proof architecture for the Riemann Hypothesis within the Weil–Connes programme, structured around seven verifiable hypotheses (H1–H7) and five supporting lemmas (A–E). Our main contributions are threefold. First, we introduce a trace–energy identity expressing the compressed trace as the square of a Hilbert–Schmidt norm, rendering Weil positivity structurally inevitable. Second, we establish Kreĭin rigidity conditions that ensure spectral stability. Third, we connect prolate spheroidal wave functions to the total positivity framework.
Geometric Transport and Trivialization of the Ground-State Bundle in the Weil-Connes Programme
Kerym Makraini
We introduce a geometric framework for the Weil-Connes programme that addresses the critical hypotheses H3 (global simplicity of the minimal eigenvalue) and H7 (identification of the Mellin limit with Riemann's Xi function). The central object is the transport integral I(Λ), which measures the cumulative distortion of the ground-state bundle over the parameter space. We prove that under certain geometric conditions, this bundle admits a trivialization consistent with the spectral interpretation of zeta zeros.