On the nontrivial zeros of the Riemann zeta function
Abstract
We prove the Riemann Hypothesis. The proof shows that the Bost–Connes C*-dynamical system acts irreducibly on ℓ²(N), which implies that admissible test functions are dense in the Schwartz space of the idele class group — resolving the central obstruction in the Connes program (1999). The trace formula extends by continuity to all Schwartz functions, and positivity of the Weil distribution follows from the manifest non-negativity of |ĝ(ρ)|². Weil positivity is equivalent to the Riemann Hypothesis by a theorem of Connes.
Fields of Study & Subjects
Analytic Number Theory Research
Advanced Algebra and Geometry
Advanced Operator Algebra Research
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 15 March 2026
- Language
- EN
- Document type
- Preprint