Constructing a Proof of the Riemann Hypothesis

This paper compares the distribution of zeros of the Riemann zeta function $ζ(s)$ with those of a symmetric combination of zeta functions, denoted ${\cal T}_+(s)$, known to have all its zeros located on the critical line $\Re(s)=1/2$. 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.

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