Small generators for S-unit groups of division algebras

Details Small generators for S-unit groups of division algebras Small generators for S-unit groups of division algebras

2012-04-26

arxiv.org/abs/1204.5968v1

Mathematics

Number Theory

Scientific paper

Let k be a number field, and suppose that B is a central simple division algebra over k. Let G be the linear algebraic group defined by the unit group B^* of B. The object of this paper is to show that the group G(O_{k,S}) of points of G over the ring O_{k,S} of S-integers of k 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 S-units.

Affiliated with

Also associated with

No associations

Rating

Small generators for S-unit groups of division algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Small generators for S-unit groups of division algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Small generators for S-unit groups of division algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-314803