On the Gross-Stark Conjecture
Samit Dasgupta, Mahesh Kakde, Kevin Ventullo
(Submitted on 26 May 2016)
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 ψ of a totally real field F. The conjecture states that after scaling by L(ψω−1,0), this value is equal to a p-adic regulator of units in the abelian extension of F cut out by ψω−1. In this paper, we prove Gross's conjecture.