Abstract

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. For a video summary of this paper, please visit https://youtu.be/hlBRUIOke04.

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