5 problems

Let $p$ be prime and let $u\in\mathbb F_p$ be a parameter for which the 15 elliptic curves obtained from the five elliptic-curve factors and the shifts $u\mapsto u-22$ and…

Let $E$ be a nonsingular elliptic curve over the rational numbers $\mathbb{Q}$ without complex multiplication and conductor $N\geq 1$. Suppose that, for primes $p$ of good reductio…

Let $A$ be a generic abelian $g$-fold over $\mathbb{Q}$, and let $\pi_{A,T}(x)$ count primes $p\leq x$ of good reduction for which $a_p(A)=T$. Write $H_A$ for the adelic Galois ima…

Akbary–Park fixed-traces conjecture. There exists a constant $C(E_1,E_2,t_1,t_2)\geq0$ such that

Refined Lang–Trotter conjecture. Uniformly in this range,