Mathematics Problem Archive

For every $\varepsilon>0$, do constants $T_0(\varepsilon),c(\varepsilon)>0$ exist such that, for $T\geq T_0$ and $H=T^{1/2+\varepsilon}$, the number $...

Let $f(x)\in\mathbb{Z}[x]$ be irreducible over $\mathbb{Q}$ with all roots real, let $f(\alpha)=0$, let $k=\mathbb{Q}(\alpha)$, and let $\mathcal{O}_k...

For $\mathcal{O}_k$ as in item 7.1, let $\Gamma_{\mathrm{unit}}$ have vertex set $\mathcal{O}_k$, joining two elements when their difference is a unit...

If $k$ is a number field that is not totally real, is there a hyperbolic $3$-manifold with trace field $k$?...