3 problems

Lang–Trotter conjecture for pairs. There exists a non-negative constant $c_{E_1,E_2}$ such that

Let $E$ and $E'$ be two elliptic curves defined over a number field $K$. Assume that $E$ and $E'$ are non-CM and non-isogenous over $\overline{\mathbb{Q}}$. Let … where…

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…