A Structural Argument for the Riemann Hypothesis: Independence, Completeness, and the Self-Mirroring Property of ½

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Authors: T.Ogawa Ogawa
Cited by: 0

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