Alladi Ramakrishnan Hall

On Gross-Stark conjecture

Mahesh Kakde

King's college London

In 1980, Gross conjectured a formula for the expected
leading term at s=0 of the p-adic L-function associated to
characters of totally real. number fields. The conjecture states a precise relation between this leading term and p-adic regulator of p-units in an abelian extension. In the talk I will present a precise formulation of the conjecture and describe its relevance
for Hilbert’s 12th problem. I will then sketch proof of this conjecture of Gross. This is a joint work with Samit Dasgupta and Kevin Ventullo.