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Universal systole bounds for arithmetic locally symmetric spaces
- Source :
- Proceedings of the American Mathematical Society. 150:795-807
- Publication Year :
- 2021
- Publisher :
- American Mathematical Society (AMS), 2021.
-
Abstract
- The systole of a closed Riemannian manifold is the minimal length of a non-contractible closed 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 a semisimple element x in SL_n(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.
- Subjects :
- Mathematics - Differential Geometry
Mathematics - Number Theory
Applied Mathematics
General Mathematics
Geometric Topology (math.GT)
Riemannian manifold
Algebraic number field
Translation (geometry)
Upper and lower bounds
Mathematics - Geometric Topology
Differential Geometry (math.DG)
Simple (abstract algebra)
Mahler measure
FOS: Mathematics
Number Theory (math.NT)
Systole
Element (category theory)
Arithmetic
Mathematics
Subjects
Details
- ISSN :
- 10886826 and 00029939
- Volume :
- 150
- Database :
- OpenAIRE
- Journal :
- Proceedings of the American Mathematical Society
- Accession number :
- edsair.doi.dedup.....6f2522cea4b3e01341b3527f83b700ea