2021/08/13 by Honnor, Matthew H. L.
#11R42 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2108.06402
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.