Let F be a totally real number field. Dasgupta conjectured an explicit p-adic analytic formula for the Gross-Stark units of F . In a later paper, Dasgupta-Spieß conjectured a cohomological formula for the principal minors and the characteristic polynomial of the Gross regulator matrix associated to a totally odd character of F . Dasgupta-Spieß conjectured that these conjectural formulas coincide for the diagonal entries of Gross regulator matrix. In this paper, we prove this conjecture when F is a cubic field.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.