General Mathematics

   

Investigation of the Characteristics of the Zeros of the Riemann Zeta Function in the Critical Strip Using Implicit Function Properties of the Real and Imaginary Components of the Dirichlet Eta Function v5

Authors: Andrew Alexander Logan

This paper investigates the characteristics of the zeros of the Riemann zeta function (of s) in the critical strip by using the Dirichlet eta function, which has the same zeros. The characteristics of the implicit functions for the real and imaginary components when those components are equal are investigated and it is shown that the function describing the value of the real component when the real and imaginary components are equal has a derivative that does not change sign along any of its individual curves - 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: 10 Pages. Typos fixed, tidying up and making the argument clearer (no change of sign)

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
[vB] 2019-02-11 15:58:25
[vC] 2019-04-19 06:17:07
[vD] 2019-05-05 04:04:13
[vE] 2019-07-01 06:29:09
[vF] 2019-09-25 05:53:13

Unique-IP document downloads: 1349 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus