Solution to the Riemann Hypothesis from geometric analysis of component series functions in the functional equation of zeta

Abstract

This paper presents a new approach towards the Riemann Hypothesis. On iterative expansion of integration term in functional equation of the Riemann zeta function we get sum of two series functions. At the `non-trivial' zeros of zeta function, value of the series is zero. Thus, Riemann hypothesis is false if that happens for an `s' off the line $\Re(s)=1/2$ ( the critical line). This series has two components $f(s)$ and $f(1-s)$. For the hypothesis to be false one component is additive inverse of the other. From geometric analysis of spiral geometry representing the component series functions $f(s)$ and $f(1-s)$ on complex plane we find by contradiction that they cannot be each other's additive inverse for any $s$, off the critical line. Thus, proving truth of the hypothesis.