School of Mathematics Colloquium

The p-adic L-functions of Kubota and Leopoldt

by Prof. Ralph Greenberg (University of Washington, USA)

Thursday, July 12, 2012 from to (Asia/Kolkata)
at Colaba Campus ( AG-69 )
Description
A good part of this talk will be an introduction to the
topic. We will discuss the p-adic analogues of the Riemann zeta function
and Dirichlet L-functions  which were constructed in the early 1960s by
Kubota and Leopoldt.    We also want to discuss a new proof of an old formula
proved by Bruce Ferrero and myself in the 1970s. That formula gives
the value of the derivative for a Kubota-Leopoldt p-adic L-function
at s=0  when the function  itself vanishes at that point. The new proof
is a joint project with Benjamin Lundell and Shaowei Zhang and relies on
studying a certain anaytic function of two p-adic variables.