2021/03/03 by Gaur, Jeet Kumar
#11M26 #FOS: Mathematics #General Mathematics (math.GM)
paper · doi:10.48550/arxiv.2103.02223
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.