3 problems

Let $D>1$ be a square-free positive integer, let $K=\mathbb{Q}(\sqrt{D})$ be the associated real quadratic field, and let $M_1(K)$ and $M_2(K)$ denote its first and second Euclidea…

Barnes–Swinnerton-Dyer conjecture. There exists a point $P_0\in\mathbb{Q}^2$ such that

Let $K$ be a number field embedded in ${\mathbb R}^n$, and let $\overline{K}={\mathbb R}^n$ be the topological closure of its image under the standard embedding. Let $M_j(K)$ and…