On the Gross-Stark Conjecture

Samit Dasgupta, Mahesh Kakde, Kevin Ventullo

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)
262 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)833-870
JournalANNALS OF MATHEMATICS
Volume188
Issue number3
Early online date22 Oct 2018
DOIs
Publication statusPublished - Nov 2018

Keywords

  • math.NT

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