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.
Citation
Samit Dasgupta. Mahesh Kakde. Kevin Ventullo. "On the Gross--Tark Conjecture." Ann. of Math. (2) 188 (3) 833 - 870, November 2018. https://doi.org/10.4007/annals.2018.188.3.3
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