Density of systoles of hyperbolic manifolds - Douba, Sami; Huang, Junzhi (Comptes Rendus. Mathématique)
We show that for each $n \ge 2$, the systoles of closed hyperbolic $n$-manifolds form a dense subset of $(0, +∞ )$. We also show that for any $n\ge 2$ and any Salem number $λ $, there is a closed arithmetic hyperbolic $n$-manifold of systole $\log (λ )$. In particular, the Salem conjecture holds if and only if the systoles of closed arithmetic hyperbolic manifolds in some (any) dimension fail to be dense in $(0, +∞ )$.