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

[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