[quote="laogui"]In fact, this Riemann Hypothesis does not exist, himself has proved the problem. Please look at https://arxiv.org/pdf/1508.02932v5.pdf.[/quote]
To understand Riemann's proof, we have to read the article that C.L.Siegel compiled according to Riemann's manuscript.

Although there is a great deal of research on Riemann's two papers, there are yet some content and formulas not being studied thoroughly. The most typical example is the following formula
$$
\pi^{-\frac{s}{2}}\Gamma(\frac{s}{2})\zeta(s)=2\Re(\pi^{-\frac{s}{2}}\Gamma(\frac{s}{2})f(s))\qquad\Re(s)=1/2,
$$
nobody has pointed out why Riemann gave it since 1932. This is Riemann's conclusion in his nachlass.

"…es ist sehr wahrscheinlich, dass alle Wurzeln reell sind. Hiervon wäre allerdings ein strenger Beweis zu wünschen; ich habe indess die Aufsuchung desselben nach einigen flüchtigen vergeblichen Versuchen vorläufig bei Seite gelassen, da er für den nächsten Zweck meiner Untersuchung entbehrlich schien."

[b]("…it is very probable that all roots are real. Of course one would wish for a rigorous proof here; I have for the time being, after some fleeting vain attempts, provisionally put aside the search for this, as it appears dispensable for the immediate objective of my investigation.") -- Bernhard Riemann

Hmm. It's probably a big mistake to claim Riemann had a proof of his conjecture (the Riemann Hypothesis) while many mathematicians including Riemann had sought a proof of Riemann Hypothesis.[/b]

[b][u]Shame on you to suggest otherwise![/u][/b]

[b]Reference link:

[url]https://en.wikipedia.org/wiki/Riemann_hypothesis#Origin[/url];

[url]https://medium.com/@JorgenVeisdal/the-riemann-hypothesis-explained-fa01c1f75d3f#.g9bwnzq0t[/url].[/b]

In fact, Riemann himself has proved the problem. Please look at https://arxiv.org/pdf/1508.02932v5.pdf

In fact, this Riemann Hypothesis does not exist, himself has proved the problem. Please look at https://arxiv.org/pdf/1508.02932v5.pdf.