Sato-tate conjecture for elliptic curves over finite fields

Question

I am doing a research project about elliptic curves over finite fields and I am across the Sato-tate conjecture, but I am having some difficulty understanding it.

What I (think) I took away from the reading: it states how the error term ($2\sqrt q$) in Hassse's theorem varies for different values of q

Any explanation or links to other references would be greatly appreciated

Answer 1

I would highly suggest Barry Mazur's "Finding meaning in error terms", Bulletin (New Series) of the American Mathematical Society, Volume 45, Number 2, April 2008, Pages 185–228.