Algebraic independence of the Kubota-Leopoldt L-functions

Abstract

The Kubota-Leopoldt p-adic L-function is regarded as a p-adic avatar of the Dirichlet L-function, in that it shares various analogous properties for special values. For example, the Kronecker limit formula holds for both complex and p-adic L-functions. I am going to give an expository introduction to another interesting topic, namely algebraic independence of the L-functions. The complex version is a consequence of universality of the functions. In the lecture, I will discuss algebraic independence of the p-adic L-functions including the mod p reduction of the p-adic L-functions.