## 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.

**Download:** **PDF**

### Submission history

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

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