Number Theory

    

The Requirements on the Non-trivial Roots of the Riemann Zeta via the Dirichlet Eta Sum

Authors: William Blickos

An explanation of the Riemann Hypothesis is given in sections, using the well known Dirichlet Eta sum equivalence, beginning with a brief history of the paper and a statement of the problem. The next 3 sections dissect the complex Eta sum into 8 real valued sums and 2 constants. Parts 6 and 8 explain a recursive relationship between the sums and constants, via 2 systems of 2 equations, while parts 7 and 9 explain the conditions generated from both systems. Finally, section 10 concludes the explanation in terms of the original inputs of the Dirichlet Eta sum, proves Riemann's suspicion, and it shows that the only possible solution for the real portion of the complex input, commonly labeled a, is that it must equal 1/2 and only 1/2.

Comments: 14 Pages.

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Submission history

[v1] 2019-09-24 21:25:35
[v2] 2020-09-02 02:41:22
[v3] 2023-12-19 04:58:22

Unique-IP document downloads: 1284 times

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