Universal Systole Bounds for Arithmetic Locally Symmetric Spaces

Abstract

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.

Publisher

American Mathematical Society

Publication Date

2-1-2022

Publication Title

Proceedings of the American Mathematical Society

Department

Mathematics

Document Type

Article

DOI

https://dx.doi.org/10.1090/proc/15683

Keywords

Reciprocal polynomials, Geometry, Lattices, Height

Language

English

Format

text

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