Number Theory


Disproof of the Riemann Zeta Function and Riemann Hypothesis (Final Revision )

Authors: Korn Rakpradit

Bernhard Riemann has written down a very mysterious work “Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse” since 1859. This paper of Riemann tried to show some functional equations related to prime numbers without proof. Let us investigate those functional equations together about how and where they came from. And at the same time let us find out whether or not the Riemann Zeta Function ζ(s)=2^s (π)^(s-1)sin(π s/2 )Г(1-s)ζ(1-s) really has zeroes at negative even integers (-2, -4 , -6 …), which are called the trivial zeroes, and the nontrivial zeroes of Riemann Zeta Function which are in the critical strip (0<ℜ(s)<1) lie on the critical line (ℜ(s) = 1/2) (or the nontrivial zeroes of Riemann Zeta Function are complex numbers of the form (1/2+∝i)).Step by step, you will not believe your eyes to see that Riemann has made such unbelievable mistakes in his work. Finally, you can easily find out that there are no trivial and nontrivial zeroes of Riemann zeta function at all.

Comments: 76 Pages.

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Submission history

[v1] 2012-06-20 21:14:40
[v2] 2012-10-01 11:30:04
[v3] 2012-10-28 02:30:49
[v4] 2012-10-31 09:19:03
[v5] 2012-11-03 04:01:51
[v6] 2012-11-06 03:35:16
[v7] 2012-11-10 01:25:40
[v8] 2012-11-16 00:52:46
[v9] 2013-01-02 07:37:06
[vA] 2013-03-27 04:16:46

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