Summer Number Theory Day; Session 4 - Derivatives of $p$-adic $L$-functions

Опубликовано 12 августа 2016, 2:03

We will discuss a new approach to proving the Ferrero-Greenberg formula for the derivative of a Kubota-Leoplodt $p$-adic $L$-function at $s=0$. The aim is to provide a proof which uses two-variable $p$-adic $L$-functions in a manner analogous to the Greenberg-Stevens proof of the Mazur-Tate-Teitelbaum conjecture for elliptic curves. In the Kubota-Leopldt setting, we use the Katz two-variable $p$-adic $L$-function attached to an imaginary quadratic field $K$. This is joint work with Ralph Greenberg and Shaowei Zhang.