General Mathematics


A Proof of the Riemann Hypothesis Version 3.1 Zeros of the Dirichlet Eta Function.

Authors: Andrew Alexander Logan

This paper investigates the characteristics of the zeros of the real component of the Riemann zeta function (of s) in the critical strip by using the real component of the Dirichlet eta function, which has the same zeros (A necessary condition for a zero of the complete function is a zero of the real component). The derivative of the real component for a fixed imaginary part of s is shown to be always positive for negative or zero values of the real component of the function, meaning that each value of the imaginary part of s produces at most one zero. Combined with the fact that the zeros of the Riemann xi function are also the zeros of the zeta function and xi(s) = xi(1-s), this leads to the conclusion that the Riemann Hypothesis is true.

Comments: 7 pages, 2 figures, corrected proof of positive derivative.

Download: PDF

Submission history

[v1] 2018-02-10 08:53:59
[v2] 2018-03-20 18:44:12
[v3] 2018-05-09 13:18:41
[v4] 2018-05-22 08:34:32
[v5] 2018-06-05 10:36:48
[v6] 2018-06-13 16:37:43
[v7] 2018-08-28 11:27:58
[v8] 2018-09-11 07:54:18
[v9] 2018-12-29 07:55:53
[vA] 2019-01-04 09:35:41

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