Universal Systole Bounds for Arithmetic Locally Symmetric Spaces
The systole of a Riemannian manifold is the minimal length of a non-contractible closed geodesic loop. We give a uniform lower bound for the systole for large classes of simple arithmetic locally symmetric orbifolds. We establish new bounds for the translation length of semisimple x is an element of SLn(R) in terms of its associated Mahler measure. We use these geometric methods to prove the existence of extensions of number fields in which fixed sets of primes have certain prescribed splitting behavior.
Lapan, Sara, Benjamin Linowitz, and Jeffrey S. Meyer. 2022. "Universal Systole Bounds for Arithmetic Locally Symmetric Spaces." Proceedings of the American Mathematical Society 150(2): 795-807.
American Mathematical Society
Proceedings of the American Mathematical Society
Reciprocal polynomials, Geometry, Lattices, Height