Stark units and special Gamma values

Abstract

In this paper we develop an effective procedure for expressing Stark units in real quadratic extensions of totally real fields as values of the Barnes multiple Gamma function at algebraic points. This procedure is used to explicitly generate non-abelian extensions of $${{\\mathbb {Q}}}$$ Q by special Gamma values. As a main component of our work, we develop an algorithm to compute Shintani sets in all dimensions.