4 problems

Generalized Sato–Tate conjecture. The moment sequence of the distributions of coefficients of the normalized L-polynomials converges to the moment sequence of the Sato–Tate group.

Algebraic Sato–Tate conjecture. The groups $\mathcal{G}_\ell$ for varying $\ell$ are all interpolated by a single algebraic group defined over $\mathbb{Q}$, called the algebraic Sa…

Let $J_9$ be the Jacobian of $C_9\colon y^2=x^9-1$, and let $\gamma$ be the matrix defined in the source's Equation (J9gamma). For matrices $U_1,U_2,U_3$ in the indicated unitary f…

Let $A$ be an abelian variety of dimension $g$, and let $\operatorname{ST}(A)$ be a maximal compact subgroup of the relevant complexified algebraic Sato–Tate group inside…