On the systole growth in congruence quaternionic hyperbolic manifolds

Abstract

We provide an explicit lower bound for the systole in principal congruence covers of compact quaternionic hyperbolic manifolds. We also prove the optimality of this lower bound.8 n(n+1) . In an appendix to this article, Dória and Murillo proved that this is the best possible constant in this case. A similar result for Hilbert modular varieties was obtained in [14].