P Adic L Functions And Algebraic Number Theory

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Lectures On P Adic L Functions Am 74 Volume 74

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Author : Kinkichi Iwasawa
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02

Lectures On P Adic L Functions Am 74 Volume 74 written by Kinkichi Iwasawa and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.

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.

Algebraic Number Fields

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Author : Albrecht Fröhlich
language : en
Publisher:
Release Date : 1977

Algebraic Number Fields written by Albrecht Fröhlich and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Mathematics categories.

P Adic L Functions And Algebraic Number Theory

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Author :
language : en
Publisher:
Release Date : 1981

P Adic L Functions And Algebraic Number Theory written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with categories.

P Adic L Functions And P Adic Representations

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Author : Bernadette Perrin-Riou
language : en
Publisher: American Mathematical Soc.
Release Date : 2000

P Adic L Functions And P Adic Representations written by Bernadette Perrin-Riou and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.

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.

Lectures On P Adic L Functions

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Author : Kenkichi Iwasawa
language : en
Publisher: Princeton University Press
Release Date : 1972-07-21

Lectures On P Adic L Functions written by Kenkichi Iwasawa and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972-07-21 with Mathematics categories.

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.

Non Archimedean L Functions

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Author : Alexei A. Panchishkin
language : en
Publisher: Springer
Release Date : 2013-11-11

Non Archimedean L Functions written by Alexei A. Panchishkin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.

1) p n=1 The set of arguments s for which ((s) is defined can be extended to all s E C,s :f:. 1, and we may regard C as the group of all continuous quasicharacters C = Hom(R~, c>

Non Archimedean L Functions And Arithmetical Siegel Modular Forms

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Author : Michel Courtieu
language : en
Publisher: Springer
Release Date : 2003-12-09

Non Archimedean L Functions And Arithmetical Siegel Modular Forms written by Michel Courtieu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-09 with Mathematics categories.

This book, now in its 2nd edition, is devoted to the arithmetical theory of Siegel modular forms and their L-functions. The central object are L-functions of classical Siegel modular forms whose special values are studied using the Rankin-Selberg method and the action of certain differential operators on modular forms which have nice arithmetical properties. A new method of p-adic interpolation of these critical values is presented. An important class of p-adic L-functions treated in the present book are p-adic L-functions of Siegel modular forms having logarithmic growth. The given construction of these p-adic L-functions uses precise algebraic properties of the arithmetical Shimura differential operator. The book will be very useful for postgraduate students and for non-experts looking for a quick approach to a rapidly developing domain of algebraic number theory. This new edition is substantially revised to account for the new explanations that have emerged in the past 10 years of the main formulas for special L-values in terms of arithmetical theory of nearly holomorphic modular forms.

Introduction To P Adic Analytic Number Theory

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Author : M. Ram Murty
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-02-09

Introduction To P Adic Analytic Number Theory written by M. Ram Murty and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-09 with Mathematics categories.

This book is an elementary introduction to $p$-adic analysis from the number theory perspective. With over 100 exercises included, it will acquaint the non-expert to the basic ideas of the theory and encourage the novice to enter this fertile field of research. The main focus of the book is the study of $p$-adic $L$-functions and their analytic properties. It begins with a basic introduction to Bernoulli numbers and continues with establishing the Kummer congruences. These congruences are then used to construct the $p$-adic analog of the Riemann zeta function and $p$-adic analogs of Dirichlet's $L$-functions. Featured is a chapter on how to apply the theory of Newton polygons to determine Galois groups of polynomials over the rational number field. As motivation for further study, the final chapter introduces Iwasawa theory.

Algebraic Number Theory

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Author : John Coates
language : en
Publisher:
Release Date : 1989

Algebraic Number Theory written by John Coates and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Algebraic number theory categories.

L Functions And Arithmetic

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Author : J. Coates
language : en
Publisher: Cambridge University Press
Release Date : 1991-02-22

L Functions And Arithmetic written by J. Coates and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-02-22 with Mathematics categories.

Aimed at presenting nontechnical explanations, all the essays in this collection of papers from the 1989 LMS Durham Symposium on L-functions are the contributions of renowned algebraic number theory specialists.