heights on algebras
generators for S-unit groups
geometry of numbers
Permanent link to this recordhttp://hdl.handle.net/20.500.12613/5905
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Abstract© 2014, University at Albany. All rights reserved. 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<sup>∗</sup><inf>S</inf> of S-units 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 S-units.
Has partNew York Journal of Mathematics
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