 

Ted Chinburg and Matthew Stover
Small generators for Sunit groups of division algebras view print


Published: 
December 1, 2014

Keywords: 
Division algebras, Sunit groups, Sarithmetic lattices, heights on algebras, generators for Sunit groups, geometry of numbers 
Subject: 
17A35, 20H10, 22E40, 11F06, 16H10, 16U60, 20F05, 11H06 


Abstract
Let k be a number field, suppose that B is a central simple division algebra over k, and choose any maximal order D of B. The object of this paper is to show that the group D_{S}* of Sunits of B is generated by elements of small height once S contains an explicit finite set of places of k. This generalizes a theorem of H. W. Lenstra, Jr., who proved such a result when B = k. Our height bound is an explicit function of the number field and the discriminant of a maximal order in B used to define its Sunits.


Acknowledgements
Chinburg partially supported by NSF Grant DMS 1100355.
Stover partially supported by NSF RTG grant DMS 0602191 and NSF grant DMS 1361000.


Author information
Ted Chinburg:
Department of Mathematics, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 10104
ted@math.upenn.edu
Matthew Stover:
Department of Mathematics, Temple University, 1805 N. Broad Street, Philadelphia, PA 19122
mstover@temple.edu

