4 problems

Let $(E,p,K)$ be a triple in which $E$ is an elliptic curve over $\mathbf{Q}$ of analytic rank $2$, $p$ is an odd prime of anomalous good ordinary reduction for $E$, and $K$ is an…

Let $E/\mathbf{Q}$ be an elliptic curve of analytic rank $2$, let $p$ be an odd prime of good ordinary anomalous reduction, and let $K$ be an imaginary quadratic field satisfying t…

Uniform-distribution conjecture. As such quadratic extensions are ordered by discriminant, $v_1-v_2$ is distributed uniformly in $\operatorname{Cl}_K$. More precisely, in the numbe…

Let $p$ and $q$ be positive integers such that $\log p/\log q$ is irrational. Let $D_q(n,i)$ denote the $i$-th digit in the canonical base-$q$ representation of $n$, and let…