On the Gross–Stark Conjecture

Abstract

In 1980, Gross conjectured a formula for the expected leading term at $s=0$ of the Deligne–Ribet $p$-adic $L$-function associated to a totally even character $\psi $ of a totally real field $F$. The conjecture states that after scaling by $L(\psi \omega ^{-1}, 0)$, this value is equal to a $p$-adic regulator of units in the abelian extension of $F$ cut out by $\psi \omega ^{-1}$. In this paper, we prove Gross’s conjecture.

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Authors

Samit Dasgupta

Duke University, Durham, NC

Mahesh Kakde

King's College London, London, England, United Kingdom

Kevin Ventullo

University of California, Los Angeles, Los Angeles, CA

Current address:

32 Shepard Street, Apt. 41, Cambridge, MA 02138