# King's College London

## On the Gross-Stark Conjecture

Research output: Contribution to journalArticle

Samit Dasgupta, Mahesh Kakde, Kevin Ventullo

Original language English 833-870 ANNALS OF MATHEMATICS 188 3 22 Oct 2018 https://doi.org/10.4007/annals.2018.188.3.3 9 Aug 2018 22 Oct 2018 Nov 2018

## Bibliographical note

38 pages

### Documents

• gross_stark15.pdf, 454 KB, application/pdf

Version:Accepted author manuscript

## 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.