3 problems

Suppose $d>0$ is a square-free integer and write $d=pm$ for an odd prime $p$ and integer $m$. If $d\equiv 1\left(\bmod{\,4}\right)$, set $\delta=1$; otherwise let $\delta=2$. Let…

Stevenhagen's conjecture. As $x\to\infty$,

Let $D\geq1$ be a fundamental discriminant, let $\mathbb{Q}(\sqrt D)$ be the associated real quadratic field, and let $\varepsilon_D$ denote its fundamental unit. Hooley–Sarnak con…