I was under the impression that in order to hit you had to have enough tracking speed to counter the target transversal velocity and your gun signature resolution should be less than the targets signature radius to ensure 100% hit ratio.

In other words vs a stationary frigate with battleship guns you would probabbly miss. But you would probabbly hit it with small guns.

Now all guns have 40000m signature resolution and I was confused, I went to read https://wiki.eveuniversity.org/Turret_Damage and am still more confused as it seems to imply that if the signature is high enough you can hit the target even if your tracking speed is less than the transversal velocity.

In another words you could use a traget painter on a frigate and hit it even if your guns couldnt track it. And also that battleship guns will 100% hit a stationary frigate.
Is this correct ?

Its best to just forget the idea of turret signature resolution, the concept was removed because it made camparing the damage application of weapons really difficult. But to address the statement, ‘sort of’, if you take a look at that wiki page, you see that angular and turret sig res are both on the numerator of the exponent (i.e. increasing either will make it harder to hit) while the tracking and sig radius are on the denominator (i.e. increasing either will make it easier to hit) so its never been a straightforward comparison of sig res vs sig radius: tracking and angular velocity also always have an effect.

Absolutely, and the best way to demonstrate this is through a DPS graph in Pyfa:

Here, my arty-fit maelstrom can’t hit this pesky frigate, moving perpendicular to me at 200m/s. At least until it gets to about 30km away from me, when the angular velocity (on the top of fraction remember!) drops low enough. But what if we turn that target painter on?

Now we’ve bloomed his sig radius by 30% (bottom of the fraction!), and we can start hitting him at about 25km now.

And yes, you will always 100% hit a target with no angular velocity (provided they are in optimal range). Take a look at the formula again. If you drop angular velocity to 0, the numerator of the fraction becomes 0. Since 0 divided by anything is 0, the entire exponent becomes 0. If we then assume you are within optimal (i.e. make the range exponent 0 as well) the formula becomes 0.5^0 = 1 i.e. a 100% chance to hit.

Disclaimers: Its important to remember that angular velocity is a mutual statistic, it is relevant to your opponent. They can be stationary and can still have angular velocity due to your own movement.

Quick summary: Tracking and Signature radius will improve your chance to hit in every case. Increasing angular velocity or gun signature resolution (not possible) will reduce it.