Number Theory

    

Solution to the Riemann Hypothesis from Geometric Analysis of Component Series Functions in the Functional Equation of Zeta

Authors: Jeet Kumar Gaur

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 function. At the ‘nontrivial’ zeros of zeta function, value of the series is zero. Thus, Riemann hypothesis is false if that happens for an ‘s’ off the line <(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.

Comments: 19 Pages.

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Submission history

[v1] 2021-02-07 18:47:46
[v2] 2021-02-10 20:17:32
[v3] 2022-03-02 18:48:35

Unique-IP document downloads: 744 times

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