The Elhaggar Interleaving Theorem: Log-Concavity, Wronskian Dynamics, and the Zeros of the Riemann Xi Function
Abstract
We establish a new interleaving theorem for the real and imaginary parts of the Riemann xi function off the critical line. The proof combines the log-concavity of the xi kernel (Csordas-Varga, 1988) with a Wronskian identity and a self-sustaining phase monotonicity argument. As a consequence, all nontrivial zeros of the Riemann zeta function lie on Re(s) = 1/2. Computational verification (7/7 checks passed) and Python code are included.
Fields of Study & Subjects
Analytic Number Theory Research
Advanced Mathematical Identities
Mathematical functions and polynomials
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 13 March 2026
- Language
- EN
- Document type
- Preprint