THE RIEMANN HYPOTHESIS FROM ARITHMETIC RIGIDITY
Abstract
Abstract. We prove the Riemann Hypothesis using the arithmetic structure of the modular surface Γ\H. The argument proceeds by contradiction: assuming a zero off the critical line creates two scattering poles with distinct Hecke eigenvalues for the same arithmetic mode. Since a single resonance cannot have two different Hecke masses, the poles must coincide, forcing all zeros to lie on Re(s) = 1/2.
Fields of Study & Subjects
Analytic Number Theory Research
Advanced Algebra and Geometry
Spectral Theory in Mathematical Physics
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 30 January 2026
- Document type
- Preprint