A Structural Argument for the Riemann Hypothesis: Independence, Completeness, and the Self-Mirroring Property of ½
Abstract
This paper presents a structural argument for the Riemann Hypothesis based on the inherent properties of prime numbers and the functional equation of the Riemann zeta function. The argument proceeds from two foundational observations: (1) prime numbers are independent and indivisible by definition, and (2) the functional equation establishes mirror symmetry around Re(s) = ½. We propose that a function built entirely from independent elements (primes) can only produce independent zeros, and that the only point where a zero can be independent (requiring no mirror partner) is where s = 1-s, which yields s = ½.
Fields of Study & Subjects
Analytic Number Theory Research
History and Theory of Mathematics
Meromorphic and Entire Functions
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 6 January 2026
- Document type
- Preprint