On the Gross-Stark Conjecture

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.

38 pages

Cited by in corpus (1)

• On the Gross order of vanishing conjecture for large vanishing orders