Number Theory

    

A Direct Proof of the Riemann Hypothesis

Authors: J N Cook with G Volk, D Allen

A function υ(s) is derived that shares all the non-trivial zeros of Riemann’s zeta function ζ(s), and a novel representation of ζ(s) is presented that relates the two. From this the zeros of ζ(s) may be grouped according to two types: υ(s)=0 and υ(s)≠0. A direct algebraic proof of the Riemann hypothesis is obtained by setting both functions to zero and solving for two general solutions for all the non-trivial zeros.

Comments: 10 Pages. Fixed minor typos, removed logic statements from body, added detail to the appendix

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Submission history

[v1] 2020-06-28 13:48:56
[v2] 2020-07-03 17:45:17
[v3] 2020-07-18 15:01:36
[v4] 2020-07-19 14:09:59
[v5] 2020-07-22 11:45:31
[v6] 2020-09-02 08:20:16
[v7] 2020-09-08 17:56:11

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