What is the Riemann Hypothesis and why is it so difficult to solve?

[lostcauses10x]

"The question is how much work does it need and if it is more efficient than other methods so as to be worth it."

The factoring of a number to see if it is prime or not is still the same with Rh if true.

Of course to find the distribution of primes that 1/2 position is interesting unto itself from the point that since 1 a factor of all the number system except zero, and by such that to show the distribution of primes it comes under the holes of the factoring greater than 1, such as the whole number system can be factored by 2, which covers 1/2 the system minus 1 dived by the total number of all primes (degree of error due to 2 is a prime: also a very very small number): , well, just maybe the part we don't see in the RH problem is how it does show the relation to the whole factoring part.

Yet even the factoring part of the whole suggest: due to the part that is undefinable small; that some non trivial zero of the Riemann zeta may be off the line of 1/2, or it is not the whole of the situation of prime distribution.

of course I am sure I lost every one with this...

 

[zetafunction]

Riemann Hypothesis in the sense of Physics IS SOLVED

http://vixra.org/pdf/1111.0105v2.pdf

1) operator -y''(x)+V(x)y(x)=E_{n}y(x) and y(x)=0=y(\infty)

2) V^{-1}(x)= 2 \sqrt \pi \frac{d^{1/2}N}{dx^{1/2}}

3) N(x) \pi = Arg\xi(1/2+i \sqrt x ) Bolte's semiclassical Law in physics

 

[atomthick]

It would be funny if from all the proved theorems that use RH we can select a group of them and say: "These theorems can't be all true at the same time unless RH is true".

 

[atomthick]

Riemann Hypothesis in the sense of Physics IS SOLVED

It's not solved it just uses the zeros on the critical line.
This doesn't prove there aren't any other zeros with the real part < 1/2

 

[PatrickPowers]

I know this is one of the famous unsolved problems still hanging around. Could someone give me the "gist" of it, and what the implications are if it is solved one way or the other? I looked it up on Wikipedia but that didn't help me much. Has anyone any idea why it is so hard to solve (i imagine it's hard )?

To me it seems like a huge coincidence. There seems no reason at all that it should be true. That could be my ignorance talking, but Littlewood said the same.

When people talk about Many Worlds I like to imagine that it really is just pure chance. So if you went to a Many Worlds conference they'd say, "So you're the guy from the world where the Reimann hypothesis is true. What's that like?"

I guess I'd say, "People go crazy trying to solve it!" and they would all gasp.

 

[lostcauses10x]

To me it seems like a huge coincidence. There seems no reason at all that it should be true. That could be my ignorance talking, but Littlewood said the same.

When people talk about Many Worlds I like to imagine that it really is just pure chance. So if you went to a Many Worlds conference they'd say, "So you're the guy from the world where the Reimann hypothesis is true. What's that like?"

I guess I'd say, "People go crazy trying to solve it!" and they would all gasp.

Think of it this way:
It goes from on form, to a different form: some were less than 1 and greater than zero. It is not difficult to think that some were between the positions the change will converge in some form. It is not just a random change.

strangly enough what is not shown in graphical relations is the first pattern carryed to the second. Thus meaning the relation of the imaginary part to the real part to the zeta values. Not an easy task. It would show a shift in the relation of i And R across the critical strip that converges to 1/2.
This is what the polar form video shows.
http://www.math.ucsb.edu/~stopple/zeta.html

Yet even with such, how to prove it converges for the infinite length of the critical strip? Well that is the problem.

 

[zetafunction]

the Riemann Xi function(s) \xi(1/2+z) and \xi(1/2+iz) can be expressed as a functional determinant of a Hamiltonian operator, functional determinants may be evaluated by zeta regularization, using in both cases the Theta functions , semiclassical and spectral ones :)

 

[zetafunction]

\xi (s) = \xi(1-s) with \frac{\xi(s)}{\xi(0)}= \frac{det(H+1/4-s(1-s))}{det(H+1/4)}

with H= - \partial _{x}^{2}+ f(x) and

f^{-1}(x)= \frac{2}{\sqrt \pi }\frac{d^{1/2}{dx^{1/2}}Arg (1/2+i \sqrt x )

http://vixra.org/abs/1111.0105