The φ(n)-Residue Framework for L-Functions: A Constructive Spectral Approach to the Riemann Hypothesis
Abstract
This preprint introduces an operator-theoretic framework for Artin L-functions based on a multiplicative boundary condition arising from Euler’s totient function. The construction is unconditional; the connection to zero distributions requires explicit analytic hypotheses. A full exposition, including the φ(n)-residue boundary, dilation symmetry, curvature estimates, and the spectral wall inequality, is provided.
Fields of Study & Subjects
Analytic Number Theory Research
Spectral Theory in Mathematical Physics
Mathematical Analysis and Transform Methods
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 15 January 2026
- Language
- EN
- Document type
- Preprint