Why is the Riemann Hypothesis (RH) true?

[Guest]

Key Ideas: k is king, and i is important/optimal...

Reference Links:


https://en.m.wikipedia.org/wiki/Riemann_hypothesis;


https://theory-of-energy.org/about/.

Very Important Reason/Answer:

The Golden (Best) Rule/Law ([tex]i = \frac{1}{2}[/tex]) of Fundamental Number Theory (Prime Number Theory) cannot be violated, and therefore, the Riemann Hypothesis is true!

The Golden Rule ([tex]i = \frac{1}{2}[/tex]) of Fundamental Number Theory:

For all positive integers, k > 1, there exists at least one prime number, p, that divides k such that either p = k or p [tex]\le k^{i }[/tex] with [tex]i= \frac{1}{2}[/tex] in accordance with the Fundamental Theorem of Arithmetic.

Remark: Despite all the deep mathematical theory about RH, the Riemann Hypothesis (RH) affirms/confirms the Golden Rule ([tex]i = \frac{1}{2}[/tex]). There are no exceptions!

Thank Lord GOD! Praise Lord GOD! Amen!

[Guest]

Remark: Theory is theory, negative or positive.

In regard to RH, there is much theory that supports it, and some doubtful 'theory' that does not...

We hope you realize/understand that RH is true!

Good Luck!

[Guest]

An explicit function is found, that accurately shows the non-trivial roots of the Riemann Zeta function and their alternation with the roots of its derivative - see the scientific forum "Riemann Hypothesis": https://dxdy.ru/topic20981-615.html and the continuation in the telegram channels https://t.me/Zeta_RH !

[Guest]

Final Remark:

It is impossible to find a nontrivial zero off the critical line ( i [tex]= \frac{1}{2}[/tex] ) for the Riemann Zeta Function!

Give up that fruitless search and stop the nonsense now and accept the very important fact that the Riemann Hypothesis is true!

Dave,

Go Blue!

[Guest]

Note: We do not confuse the variable, i, with the imaginary symbol, i.

[Guest]

Note: We do not confuse the variable, i, with the imaginary symbol, i.

To avoid any further confusion, we let [tex]h = \frac{1}{2}[/tex] to define the critical line for all nontrivial zeros of the Riemann Zeta Function.

[Guest]

FYI: On the Riemann Zeta Function and its complex nontrivial zeros, the truth/certainty of the Riemann Hypothesis, the Fundamental Theorem of Arithmetic, and the Harmonic Series:

We denote the complex nontrivial zeros (conjugate pairs) of the Riemann Zeta Function assuming the Riemann Hypothesis:

[tex]z = \frac{1}{2} + bi[/tex] and [tex]\overline{z} = \frac{1}{2} - bi[/tex] with [tex]z + \overline{z} =1[/tex]

where [tex]\sum_{k=1}^{ \infty } \frac{1}{k^{z}} = 0[/tex] and [tex]\sum_{k=1}^{ \infty } \frac{1}{k^{\overline{z}}} = 0[/tex] .

And thus, [tex]\sum_{k=1}^{ \infty } \frac{1}{k^{z}} \frac{1}{k^{\overline{z}}} = \sum_{k=1}^{ \infty } \frac{1}{k^{z + \overline{z} }} = \sum_{k=1}^{ \infty } \frac{1}{k} = \infty[/tex] (the very important Harmonic Series).


The Riemann Hypothesis is true! And we rest our case. Amen!

Dave,

Go Blue!

[Guest]

That last post must be the shortest proof (support) of the Riemann Hypothesis! Go figure!

[Guest]

That last post must be the shortest proof (support) of the Riemann Hypothesis (RH)! Go figure!

In a nutshell, the truth of RH (Re(z) = Re([tex]\overline{z}[/tex]) = [tex]\frac{1}{2}[/tex]) if and only if the divergent Harmonic Series ([tex]\sum_{k=1}^{ \infty } \frac{1}{k} = \infty[/tex]).

[Guest]

WOW! (Words of Wisdom): There are no counterexamples to the Riemann Hypothesis!

[Guest]

WOW! (Words Of Wisdom!): There are no counterexamples to the Riemann Hypothesis (RH)!

The truth of RH is bound by the truth of the divergent Harmonic Series, and therefore, there are no exceptions (counterexamples) to RH.

[Guest]

WOW! (Words Of Wisdom!): There are no counterexamples to the Riemann Hypothesis (RH)!

The truth of RH is bound by the truth of the divergent Harmonic Series, and therefore, there are no exceptions (counterexamples) to RH.

Moreover, the truth of the divergent Harmonic Series is bound by the truth of RH.

They are bound together in truth and in harmony forever. Amen!

"For those who love God, all things must work together for the best." -- Romans 8:28.

Thank Lord GOD! Praise Lord GOD! Amen!

[Guest]

An Important Update:

In a nutshell, the truth of RH (Re(z) = Re([tex]\overline{z}[/tex]) = [tex]\frac{1}{2}[/tex] when [tex]\sum_{k=1}^{ \infty } \frac{1}{k^{z}} = 0[/tex] and [tex]\sum_{k=1}^{ \infty } \frac{1}{k^{\overline{z}}} = 0[/tex]) if and only if the divergent Harmonic Series ([tex]\sum_{k=1}^{ \infty } \frac{1}{k} = \infty[/tex]) exists.

[Guest]

Update:

In a nutshell, the Riemann Hypothesis is true if and only if the divergent Harmonic Series exists.

[Guest]

Update:

In a nutshell, the divergent Harmonic Series exists if and only if the Riemann Hypothesis is true .

[Guest]

Watch: The Riemann Hypothesis, Explained.

Enjoy!

[Guest]

FYI: A Few Words About Author