4 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 $E$ be the elliptic curve and let $X_{\infty,f}^{\pm}$, $\Lambda(H)$, and the groups and fields denoted by the notation of Section 1 in the source be as defined there.…

Let $k$ be an algebraically closed field of positive characteristic $p>0$, and let $C$ be a proper smooth curve over $k$ with function field $K=k(C)$. Let $X$ be a non-isotrivial,…