2 edition of **Lectures on p-adic L-functions.** found in the catalog.

Lectures on p-adic L-functions.

Kenkichi Iwasawa

- 7 Want to read
- 32 Currently reading

Published
**1972** by Princeton University Press in Princeton, N.J .

Written in English

- Algebraic number theory,
- L-functions

**Edition Notes**

Series | Annals of mathematics studies, no. 74 |

The Physical Object | |
---|---|

Pagination | 106p. |

Number of Pages | 106 |

ID Numbers | |

Open Library | OL14811182M |

Introduction to p-adic Analytic Number Theory by M. Ram Murty, , available at Book Depository with free delivery : M. Ram Murty. @incollection {deligne, MRKEY = {}, AUTHOR = {Deligne, P.}, TITLE = {Le groupe fondamental de la droite projective moins trois points},Cited by: Math P { Representation theory of p-adic groups { Fall References on representation theory of p-adic groups: We will be discussing material taken from the following sources: J. N. Bernstein, Representations of p-adic groups, Notes taken by K. Rumelhart of lectures by J. Bernstein at Harvard in the Fall of The p-Adic L-Functions of Modular Elliptic Curves 3 Prompted by the role of the p-adic uniformisation (1) in [BD98] and [BD99], Iovita and Spiess independently proposed a construction of the p- adic L-function of [BD96] following Schneider’s construc-tion,presentedin[BDIS]andrecalledinSection,clariﬁedtheroleof p-adic integration in the .

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In mathematics, a p-adic zeta function, or more generally a p-adic L-function, is a function analogous to the Riemann zeta function, or more general L-functions, but whose domain and target are p-adic (where p is a prime number).For example, the domain could be the p-adic integers Z p, a profinite p-group, or a p-adic family of Galois representations, and the image.

Lectures on P-Adic L-Functions. (AM), Volume 74 - Ebook written by Kinkichi Iwasawa. Read this book using Google Play Books app on your PC, android, iOS devices.

Download for offline reading, highlight, bookmark or take notes while you read Lectures on P-Adic L-Functions. (AM), Volume An especially timely work, the book is an introduction to the theory of p-adic L-functions originated by Kubota and Leopoldt in 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. An especially timely work, the book is an introduction to the theory of p-adic L-functions originated by Kubota and Leopoldt in 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.

An especially timely work, the book is an introduction to the theory of p-adic L-functions originated by Kubota and Leopoldt in as p-adic analogues Lectures on p-adic L-functions. book the classical L-functions of sor 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. Lectures on p-adic L-functions. [Kenkichi Iwasawa] Home. WorldCat Home About WorldCat Help. Search. Search for Library Items Search for Lists Search Lectures on p-adic L-functions.

book Book, Internet Lectures on p-adic L-functions. book All Authors / Contributors: Kenkichi Iwasawa. Find more information about: ISBN: OCLC Number.

These are notes of lectures given at Princeton University during the fall semester of The notes present an introduction to p-adic L-functions originated in Kubota-Leopoldt {10} as p-adic analogues of classical L-functions of by: These are notes of lectures given at Princeton University during the fall semester of The notes present an introduction to p-adic L-functions originated in Kubota-Leopoldt {10} as p-adic analogues of classical L-functions of Dirichlet.

Lectures on p-adic L-functions Add library to Favorites Please choose whether or not you want other users to be able to see on your profile that this library is a favorite of yours.

Lectures on P-Adic L-Functions. (AM), Volume 74 by Kinkichi Iwasawa,available at Book Depository with free delivery worldwide. 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 ofBrand: Springer-Verlag New York. What corresponds for p-adic L-functions. Essentially there isn't anything that matches. You can sit in many lectures on p-adic L-functions without seeing anything that merits the name "function", in the sense of function theory.

What lies behind this. It is not that p-adic numbers are less "explicit" than complex numbers at all. An especially timely work, the book is an introduction to the theory of p-adic L-functions originated by Kubota and Leopoldt in as p-adic analogues of, ISBN Buy the Lectures on P-Adic L-Functions.

JOURNAL OF NUMBER THEORY 8, () A Note On p-adic L-Functions* L. WASHINGTON' Department of Mathematics, Princeton University, Princeton, New Jersey Communicated by H. Leopoldt Received Febru An elementary proof is given for the existence of the Kubota-Leopoldt p-adic by: Lectures on P-Adic L-Functions.

(AM), Volume Series:Annals of Mathematics Studies Book Book Series. Frontmatter. Pages i-iv. Download PDF. Free Access; PREFACE. GENERALIZED BERNOULLI NUMBERS.

Pages Get Access to Full Text §3. p-ADIC L-FUNCTIONS. Pages Get Access to Full Text §4. p-ADIC LOGARITHMS AND p. AN INTRODUCTION TO p-ADIC L-FUNCTIONS 5 Remark —Something that both (a) and (b) have in common is their use of p-adic L-functions.

In fact, there is a p-adic version of Birch and Swinnerton-Dyer, due to Mazur, Tate and Teitelbaum (see [MTT86]), which relates the rank of the p-Selmer group to the order of vanishing of a p-adic L-function.

Actually, p-adic L-functions are expected to satisfy functional equations compatible with the classical M an ordinary motive, Coates and Perrin-Riou conjectured the interpolation property at critical integers and the expected functional equation in some papers in the early nineties (see for example this).In particular, the Kubota-Leopoldt p-adic L-functions interpolate.

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 work on Hecke polynomials. Lectures on P-Adic L-F My Searches (0) My Cart Added To Cart Check Out.

Menu. Subjects. Architecture and Design; Arts; Lectures on P-Adic L-Functions. (AM), Volume Series:Annals of Mathematics Studies Book Book Series. An especially timely work, the book is an introduction to the theory of p-adic L-functions originated by Kubota and Leopoldt in as p-adic analogues of the classical L-functions of sor Iwasawa reviews the classical results on Dirichlet's L-functions and sketches a proof for some of them.

In this section, we deﬁne the p-adic Euler L-functions and compute its value at negativ e integers. Given x ∈ Z p, p ∤ x and p > 2, there exists a unique (p − 1)-th ro ot of. p-adic L-functions for GL(n) These are the expanded notes of a mini-course of four lectures by the same title given in the workshop "p-adic aspects of modular forms" held at IISER Pune, in.

Lectures on p-adic Differential Equations (Grundlehren der mathematischen Wissenschaften) 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. P Cited by: L-function is deﬁned. I am following Iwasawa’s red book [Iwa72] for the classic construction. Chapter III: Stickelberger Elements and p-adic L-Functions. Here the sec-ond construction is presented. The main technical tool is Theorem which relates a power series to an element of a group algebra.

The p-adic L-function will arise in File Size: KB. These notes represent an expanded form of lectures given at the U. in Strasbourg during the fall term of 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. pp-adic L-functions and Iwasawa main conjectures - Zheng Liu Zheng Liu.

later by Iwasawa who established much of the groundwork of a p-adic analytic number theory. Thus, the search for p-adic incarnations of the classical zeta and L-functions is of relatively recent origin and has been a useful motif in the study of special values of various L-functions and their arithmetic Size: KB.

$\begingroup$ Look in the chapter on p-adic L-functions in Washington's book on cyclotomic fields, e.g., section on applications of the p-adic class number formula.

$\endgroup$ – KCd May 9 '13 at AN INTRODUCTION TO p-ADIC L-FUNCTIONS 5 Remark Something that both (a) and (b) have in common is their use of p-adic L-functions. In fact, there is a p-adic version of Birch and Swinnerton-Dyer, due to Mazur, ateT. Description; Chapters; Supplementary; The aim of this book is to give a systematic exposition of results in some important cases where p-adic families and p-adic L-functions are first look at p-adic families in the following cases: general linear groups, symplectic groups and definite unitary also look at applications of this theory to.

p-adic cohomology: from theory to practice Kiran S. Kedlaya1 Introduction These notes (somewhat revised from the version presented at the AWS) present a few facets of the relationship between p-adic analysis, algebraic de Rham cohomology, and zeta functions of algebraic varieties.

A key theme is the explicit,Cited by: 6. Notes on p-adic L-functions 3 { with a continuous, E -linear G Q-action ˆ: G Q!Aut E (H (M)); together with maps I 1and I for each nite place of E, all satisfying the following compatibility requirements: H (M) are compatible in the following sense: { there is a nite set Sof nite primes of Q such that for every p62Sand every nite.

Open Library is an open, editable library catalog, building towards a web page for every book ever published. Author of Lectures on p-adic L-functions, Papers, Local Classfield Theory (Oxford Mathematical Monograph), Kenkichi Iwasawa Collected Papers, Local class field theory, Algebraic number theory--in honor of K.

Iwasawa, Algebraic functions. Abstract. We would like to describe several results concerninq certain ℤ p 2-extensions which come from imaginary quadratic motivation for our results is to provide some evidence for a “two-variable main conjecture” that has been suggested at Cited by: 1.

Open Math Notes. AMS Open Math Notes is a repository of freely downloadable mathematical works in progress hosted by the American Mathematical Society as a service to researchers, teachers and students.

Bestsellers Sale. Enjoy 40% off. Destination page number Search scope Search Text Search scope Search Text. Schikhof gives constructions of p-adic Gamma and Zeta functions and develops enough integration theory to allow the reader to follow the measure-theoretic approach to p-adic L-functions.

He even does a little bit with p-adic differential equations. Though the book is labelled "an introduction," the pre-requisites are quite heavy. The p-adic L-functions of modular elliptic curves satisfactory theory of p-adic L-functions in the cyclotomic context.

To bring the p-adic L-function of Manin and Mazur–Swinnerton-Dyer more in line with Schneider’s approach, and reconcile the ostensibly disparate. The aim of this book is to give a systematic exposition of results in some important cases where p-adic families and p-adic L-functions are studied.

We first look at p-adic families in the following cases: general linear groups, symplectic groups and definite unitary groups. We also look at applications of this theory to modularity lifting. The Artin L-function (,) is then the infinite product over all prime ideals of these factors. As Artin reciprocity shows, when G is an abelian group these L-functions have a second description (as Dirichlet L-functions when K is the rational number field, and as Hecke L-functions in.

Transcendental Numbers. (AM) - Ebook written by Carl Ludwig Siegel. Read this book using Google Play Books app on your PC, android, iOS devices.

Download for offline reading, highlight, bookmark or take notes while you read Transcendental Numbers. (AM).Author: Carl Ludwig Siegel.This book grew. out of lectures given at the University of Maryland in / The purpose was to give a treatment of p-adic L-functions and cyclotomic fields, including Iwasawa's theory of Zp-extensions, which was accessible to mathematicians .Older Publications (More than 5 years old) These works are supported partially by various NSF grants as acknowledged in each article.

H. Hida, On the values of Hecke's L-functions at non-positive integers, J. Math. Soc. Japan, 30 (), [Euclid site] H. Hida, On abelian varieties with complex multiplication as factors of the abelian variety attached to Hilbert .