We obtain new results concerning the Sato–Tate conjecture on the distribution of Frobenius traces over single and double parametric families of elliptic curves. We consider these curves for values of parameters having prescribed arithmetic structure: product sets, geometric progressions, and most significantly prime numbers. In particular, some families are much thinner than the ones previously studied.
- Parametric families of elliptic curves
- Sato–Tate conjecture