Lectures On P Adic L Functions
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Lectures on P-adic L-functions
Author: Kenkichi Iwasawa
language: en
Publisher: Princeton University Press
Release Date: 1972-07-21
An especially timely work, the book is an introduction to the theory of p-adic L-functions originated by Kubota and Leopoldt in 1964 as p-adic analogues of the classical L-functions of Dirichlet. Professor Iwasawa reviews the classical results on Dirichlet's L-functions and sketches a proof for some of them. Next he defines generalized Bernoulli numbers and discusses some of their fundamental properties. Continuing, he defines p-adic L-functions, proves their existence and uniqueness, and treats p-adic logarithms and p-adic regulators. He proves a formula of Leopoldt for the values of p-adic L-functions at s=1. The formula was announced in 1964, but a proof has never before been published. Finally, he discusses some applications, especially the strong relationship with cyclotomic fields.
Lectures on P-Adic L-Functions
Author: Kinkichi Iwasawa
language: en
Publisher: Princeton University Press
Release Date: 2016-03-02
An especially timely work, the book is an introduction to the theory of p-adic L-functions originated by Kubota and Leopoldt in 1964 as p-adic analogues of the classical L-functions of Dirichlet. Professor Iwasawa reviews the classical results on Dirichlet's L-functions and sketches a proof for some of them. Next he defines generalized Bernoulli numbers and discusses some of their fundamental properties. Continuing, he defines p-adic L-functions, proves their existence and uniqueness, and treats p-adic logarithms and p-adic regulators. He proves a formula of Leopoldt for the values of p-adic L-functions at s=1. The formula was announced in 1964, but a proof has never before been published. Finally, he discusses some applications, especially the strong relationship with cyclotomic fields.
$p$-adic $L$-Functions and $p$-adic Representations
Author: Bernadette Perrin-Riou
language: en
Publisher: American Mathematical Soc.
Release Date: 2000
Traditionally, p-adic L-functions have been constructed from complex L-functions via special values and Iwasawa theory. In this volume, Perrin-Riou presents a theory of p-adic L-functions coming directly from p-adic Galois representations (or, more generally, from motives). This theory encompasses, in particular, a construction of the module of p-adic L-functions via the arithmetic theory and a conjectural definition of the p-adic L-function via its special values. Since the original publication of this book in French (see Astérisque 229, 1995), the field has undergone significant progress. These advances are noted in this English edition. Also, some minor improvements have been made to the text.