On optimal embeddings and trees
Number Theory
2016-06-22 v1
Abstract
We apply the theory of Bruhat-Tits trees to the study of optimal embeddings of two and three dimensional commutative orders into quaternion algebras. Specifically, we determine how many conjugacy classes of global Eichler orders in a quaternion algebra yield optimal representations of such orders. This completes the previous work by C. Maclachlan, who considered only Eichler orders of square free level and integral domains as sub-orders. The same technique is used in the second part of this work to compute local embedding numbers, extending previous results by J. Brzezinski.
Keywords
Cite
@article{arxiv.1606.06396,
title = {On optimal embeddings and trees},
author = {Manuel Arenas and Luis Arenas-Carmona and Jaime Contreras},
journal= {arXiv preprint arXiv:1606.06396},
year = {2016}
}