Lectures On P Adic L Functions

DOWNLOAD

Download Lectures On P Adic L Functions PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Lectures On P Adic L Functions book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

Lectures On P Adic L Functions

DOWNLOAD
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.

Lectures On P Adic L Functions

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

Lectures On P Adic L Functions 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.

P Adic L Functions And P Adic Representations

DOWNLOAD
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.

P Adic Numbers P Adic Analysis And Zeta Functions

DOWNLOAD
Author : Neal Koblitz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

P Adic Numbers P Adic Analysis And Zeta Functions written by Neal Koblitz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Neal Koblitz was a student of Nicholas M. Katz, under whom he received his Ph.D. in mathematics at Princeton in 1974. He spent the year 1974 -75 and the spring semester 1978 in Moscow, where he did research in p -adic analysis and also translated Yu. I. Manin's "Course in Mathematical Logic" (GTM 53). He taught at Harvard from 1975 to 1979, and since 1979 has been at the University of Washington in Seattle. He has published papers in number theory, algebraic geometry, and p-adic analysis, and he is the author of "p-adic Analysis: A Short Course on Recent Work" (Cambridge University Press and GTM 97: "Introduction to Elliptic Curves and Modular Forms (Springer-Verlag).

P Adic Analysis

DOWNLOAD
Author : Neal Koblitz
language : en
Publisher: Cambridge University Press
Release Date : 1980-11-28

P Adic Analysis written by Neal Koblitz 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 1980-11-28 with Mathematics categories.

An introduction to recent work in the theory of numbers and its interrelation with algebraic geometry and analysis.

Lectures On P Adic Differential Equations

DOWNLOAD
Author : Bernard Dwork
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Lectures On P Adic Differential Equations written by Bernard Dwork and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

The present work treats p-adic properties of solutions of the hypergeometric differential equation d2 d ~ ( x(l - x) dx + (c(l - x) + (c - 1 - a - b)x) dx - ab)y = 0, 2 with a, b, c in 4) n Zp, by constructing the associated Frobenius structure. For this construction we draw upon the methods of Alan Adolphson [1] in his 1976 work on Hecke polynomials. We are also indebted to him for the account (appearing as an appendix) of the relation between this differential equation and certain L-functions. We are indebted to G. Washnitzer for the method used in the construction of our dual theory (Chapter 2). These notes represent an expanded form of lectures given at the U. L. P. in Strasbourg during the fall term of 1980. We take this opportunity to thank Professor R. Girard and IRMA for their hospitality. Our subject-p-adic analysis-was founded by Marc Krasner. We take pleasure in dedicating this work to him. Contents 1 Introduction . . . . . . . . . . 1. The Space L (Algebraic Theory) 8 2. Dual Theory (Algebraic) 14 3. Transcendental Theory . . . . 33 4. Analytic Dual Theory. . . . . 48 5. Basic Properties of", Operator. 73 6. Calculation Modulo p of the Matrix of ~ f,h 92 7. Hasse Invariants . . . . . . 108 8. The a --+ a' Map . . . . . . . . . . . . 110 9. Normalized Solution Matrix. . . . . .. 113 10. Nilpotent Second-Order Linear Differential Equations with Fuchsian Singularities. . . . . . . . . . . . . 137 11. Second-Order Linear Differential Equations Modulo Powers ofp ..... .

Cyclotomic Units And P Adic L Functions

DOWNLOAD
Author : Julian Christiansen Horn
language : en
Publisher:
Release Date : 1976

Cyclotomic Units And P Adic L Functions written by Julian Christiansen Horn and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with categories.

Elementary Theory Of L Functions And Eisenstein Series

DOWNLOAD
Author : Haruzo Hida
language : en
Publisher: Cambridge University Press
Release Date : 1993-02-11

Elementary Theory Of L Functions And Eisenstein Series written by Haruzo Hida 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 1993-02-11 with Mathematics categories.

The theory of p-adic and classic modular forms, and the study of arithmetic and p-adic L-functions has proved to be a fruitful area of mathematics over the last decade. Professor Hida has given courses on these topics in the USA, Japan, and in France, and in this book provides the reader with an elementary but detailed insight into the theory of L-functions. The presentation is self contained and concise, and the subject is approached using only basic tools from complex analysis and cohomology theory. Graduate students wishing to know more about L-functions will find that this book offers a unique introduction to this fascinating branch of mathematics.

P Adic Numbers

DOWNLOAD
Author : Fernando Quadros Gouvea
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

P Adic Numbers written by Fernando Quadros Gouvea and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

In the course of their undergraduate careers, most mathematics majors see little beyond "standard mathematics:" basic real and complex analysis, ab stract algebra, some differential geometry, etc. There are few adventures in other territories, and few opportunities to visit some of the more exotic cor ners of mathematics. The goal of this book is to offer such an opportunity, by way of a visit to the p-adic universe. Such a visit offers a glimpse of a part of mathematics which is both important and fun, and which also is something of a meeting point between algebra and analysis. Over the last century, p-adic numbers and p-adic analysis have come to playa central role in modern number theory. This importance comes from the fact that they afford a natural and powerful language for talking about congruences between integers, and allow the use of methods borrowed from calculus and analysis for studying such problems. More recently, p-adic num bers have shown up in other areas of mathematics, and even in physics.

13 Lectures On Fermat S Last Theorem

DOWNLOAD
Author : Paulo Ribenboim
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

13 Lectures On Fermat S Last Theorem written by Paulo Ribenboim and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Lecture I The Early History of Fermat's Last Theorem.- 1 The Problem.- 2 Early Attempts.- 3 Kummer's Monumental Theorem.- 4 Regular Primes.- 5 Kummer's Work on Irregular Prime Exponents.- 6 Other Relevant Results.- 7 The Golden Medal and the Wolfskehl Prize.- Lecture II Recent Results.- 1 Stating the Results.- 2 Explanations.- Lecture III B.K. = Before Kummer.- 1 The Pythagorean Equation.- 2 The Biquadratic Equation.- 3 The Cubic Equation.- 4 The Quintic Equation.- 5 Fermat's Equation of Degree Seven.- Lecture IV The Naïve Approach.- 1 The Relations of Barlow and Abel.- 2 Sophie Germain.- 3 Co.