Constructing a Proof of the Riemann Hypothesis

Abstract

This paper compares the distribution of zeros of the Riemann zeta function ζ(s) with those of a symmetric combination of zeta functions, denoted T + (s), known to have all its zeros located on the critical line ℜ(s) = 1/2. Criteria are described for constructing a suitable quotient function of these, with properties advantageous for establishing an accessible proof that ζ(s) must also have all its zeros on the critical line: the celebrated Riemann hypothesis. While the argument put forward is not at the level of rigour required to constitute a full proof of the Riemann hypothesis, it should convince non-specialists that it must hold.