Sato-Tate conjecture

The Sato-Tate conjecture concerns the distribution of certain numbers called eigenvalues associated with mathematical objects known as elliptic curves. These eigenvalues can be thought of as representing angles that fall within a specific range. The conjecture predicts that, across many such elliptic curves, these angles are spread out in a specific, predictable pattern similar to how points are scattered evenly on a circle. Confirmed in recent years, this pattern helps mathematicians understand the underlying symmetry and structure of elliptic curves, which are fundamental in number theory and have applications in cryptography.