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On the Gross-Stark Conjecture

Research output: Contribution to journalArticle

Samit Dasgupta, Mahesh Kakde, Kevin Ventullo

Original languageEnglish
Pages (from-to)833-870
JournalANNALS OF MATHEMATICS
Volume188
Issue number3
Early online date22 Oct 2018
DOIs
Accepted/In press9 Aug 2018
E-pub ahead of print22 Oct 2018
PublishedNov 2018

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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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