Systole of congruence coverings of arithmetic hyperbolic manifolds
Systole of congruence coverings of arithmetic hyperbolic manifolds
In this paper we prove that, for any arithmetic hyperbolic n -manifold M of the first type, the systole of most of the principal congruence coverings M_{I} satisfy \mathrm{sys}(M_{I})\geq \frac{8}{n(n+1)}\mathrm{log}(\mathrm{vol}(M_{I}))-c, where c is a constant independent of I . This generalizes previous work of Buser and Sarnak, and Katz, Schaps, …