This blog is about the nature of things including ourselves.


“We must know;  we shall know.”  — David Hilbert.

“When the solution is simple, GOD is answering.”  — Albert Einstein.

Riemann Hypothesis states that the real part of all nontrivial zeros,

s = a ± b * i,

of the Riemann zeta function equals one-half (a = 1/2)  where 

Re(s = a ± b * i) = a,

and where the Riemann zeta function is  Σ 1/k^s  (from k = 1 to k = ∞).


Reference links:

Riemann Hypothesis;

Why is the Riemann Hypothesis true?;

Subtle relations: prime numbers, complex functions, energy levels and Riemann;

150 Years of Riemann Hypothesis;

Turing and the Computational Tradition in Pure Mathematics (http://www.computing-conference.ugent.be/file/16).


*****

“… deepest interrelationships in analysis are of an arithmetical nature.”  — Hermann Minkowski.

In the simplest sense, the Riemann Hypothesis (RH) confirms for all positive integers,  k > 1,

there exists a prime, p, which divides k such that either

p = k

or

p ≤ k^( 1/2 = a = Re(s = a ± b * i) )

where s is the nontrivial zero of the Riemann zeta function.

Furthermore, only s + s’ = 1  over 0 ≤ a ≤ 1 satisfies the  divergent Euler zeta function (Harmonic Series) for which there exists infinitely prime numbers (see Euler’s proof)  where a = 1/2.  

Hence, s = 1/2 + b * i and s’ = 1/2 – b* i are the only nontrivial zeta zeros of the Riemann zeta function in the interval, 0 ≤ a ≤ 1.

Note:  s = a + b * i and s’ = a – b* i are the nontrivial zeta zeros of the Riemann zeta function in the interval, 0 ≤ a ≤ 1.

Therefore, the answer is affirmative.

The Riemann Hypothesis is true!   — David Cole.

“If you can’t explain simply, you don’t understand it well enough.” — Albert Einstein.


Reference Links:

What is the correct proof of the famous and important Polignac Conjecture?.

Romans 8:28

*****

Keep an Open Mind!


(W)ork has degrees of organization according to (M)atter and (E)nergy.

Furthermore, work has various degrees of organization involving complex processes undergoing change or resistance to change…

1.  W = M + E;  (Work is a manifold or network of matter (mass) and energy in a physical system.)

2.  (dW)^2 = ME,  0 < || d ||^2 < 1/4;

3.  ΔE = c^2 * ΔM (Einstein’s Equation);

4.  E`  =  (ΔM`*h)^2 + Ah^4 (Higg’s Equation);

5.  Schrödinger’s Wave Equation!

Postulate Zero or Omega Postulate:  Aether exists, and it is also called UnConditional Reality (UCR or GOD).

Postulate One (Conditional Reality (CR)):  All states of a physical system are temporal or changing.

Postulate Two (CR):  Matter and Energy are more or less organizing, and they define the geometry or shape of space.

Postulate Three (CR):  Forces arise due to Matter and Energy interaction or conversion.

Postulate Four (CR):  There is no net accumulation of Matter or Energy at any point in system.

Note:  Gravity works!  It insures system integrity of our world of work while Lord GOD works out its perfection according to HIS Image (Unconditional).                   — David Cole.

“Try and penetrate with our limited means the secrets of nature, and you will find that, behind all the discernible laws and connections, there remains something subtle, intangible, and inexplicable. Veneration for this force beyond anything we can comprehend is my religion.”  — Albert Einstein