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 8 parts, with the first being a statement of the problem. In the next 3 parts, the complex valued Dirichlet Eta sum, a known equivalence to Riemann Zeta in the critical strip, is split into 8 real valued sums and 2 constants. Part 5 explains a recursive relationship between the 8 sums. Section 6 shows that the sums must individually equal 0. Part 7 details the ratios of the system when all sums equal 0 at once. Finally, part 8 solves the system in terms of the original Dirichlet Eta sum inputs. The result 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 thus proves Riemann’s suspicion.

Comments: 11 Pages.

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Submission history

[v1] 2019-09-24 21:25:35

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