Explicit computation of Gross–Stark units over real quadratic fields

TextWe present an effective and practical algorithm for computing Gross–Stark units over a real quadratic base field FF. Our algorithm allows us to explicitly construct certain relative abelian extensions of FF where these units lie, using only information from the base field. These units were recently proved to always exist within the correct extension fields of FF by Dasgupta, Darmon, and Pollack, without directly producing them.VideoFor a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=8h1-GW-sTNc.