2 problems

The discrepancy bound conjecture. For every integer $s\geq1$ and every $\epsilon>0$, there exists a constant $C=C(E,s,\epsilon)$ such that, for every integer $K\geq1$,

The Sato–Tate independence conjecture. For every integer $s\geq1$, the sequence $\{X_k\}_{k\geq1}$ is uniformly distributed with respect to $\mu_{ST}^{[s]}$; equivalently,