On the Gross–Stark Conjecture


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.


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

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