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arXiv · 1204.5968

Small generators for S-unit groups of division algebras

Ted Chinburg·Matthew Stover
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Abstract

Let $k$ be a number field, suppose that $B$ is a central simple division algebra over $k$, and choose any maximal order $\mathcal{D}$ of $B$. The object of this paper is to show that the group $\mathcal{D}_S^*$ 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.

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Ted Chinburg, Matthew Stover. 2014-11-28. Small generators for S-unit groups of division algebras. https://arxiv.org/abs/1204.5968

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