General Mathematics


A Proof of the Riemann Hypothesis Version 2.1

Authors: Andrew Alexander Logan

This paper investigates the characteristics of the Riemann xi function. A detailed investigation of two integration approaches to Riemann's original equation (firstly as a series including incomplete gamma functions and secondly as a power series), focussing firstly on the characteristics of the expressions including incomplete gamma functions (highlighting the properties of the continued fraction components as the components are varied and the characteristics of the series terms as they reduce rapidly in magnitude) and secondly on the implications of the power series representation in the case where the imaginary component is zero leads to the conclusion that the Riemann xi function only has real zeros.

Comments: 14 Pages, 19 Figures - Additional Argument for no additional real zeros when imaginary component varied from zero (based on relative sizes of continued fraction and other components). I think it's all there now!

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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

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