5 problems

Let $E/\mathbb{Q}$ be a CM elliptic curve, let $r\neq 0$ be a fixed integer, let $C_{E,r}$ be the Lang–Trotter constant, and let $\overline{\omega}_{E,r}$ be the explicit constant…

Let $E$ be an elliptic curve over ${\mathbb Q}$, and let $a_p(E)$ denote the trace of Frobenius of $E$ at a prime $p$ of good reduction. An integer $a$ is subject to a congruence o…

Let $A$ be a principally polarized abelian variety over $\mathbb Q$ of dimension $g\geq 1$, with conductor $N_A$, and let $\rho_A$ be the product of its $\ell$-adic Galois represen…

Lang–Trotter fixed-Frobenius-field conjecture. There exists a constant $C(E,F)>0$ such that

Let $A$ be the coefficient ring of a global function field $F$, let $q$ be the size of its constant field, and let $\phi$ be a Drinfeld module over $F$. Fix $t\in A$, and let…