Iwasawa theory and modular forms

Author(s)

• 黒川, 信重 クロカワ, ノブシゲ
• 栗原, 将人 クリハラ, マサト
• 斎藤, 毅 サイトウ, タケシ
• Kuwata, Masato

Bibliographic Information

Iwasawa theory and modular forms

Nobushige Kurokawa, Masato Kurihara, Takeshi Saito ; translated from the Japanese by Masato Kuwata

（Translations of mathematical monographs, v. 242 . Number theory ; 3）（Iwanami series in modern mathematics）

American Mathematical Society, c2012

Other Title

数論. 3 : 岩澤理論と保型形式

Sūron

Note

"Originally published in Japanese by Iwanami Shoten, publishers, Tokyo, 1998 and 2005"--T.p. verso

Original Japanese ed. published as no. 20 in the series: 岩波講座現代数学の基礎

Includes bibliographical references (p. 211-215) and index

Description and Table of Contents

Description

This is the third of three related volumes on number theory. (The first two volumes were also published in the Iwanami Series in Modern Mathematics, as volumes 186 and 240.) The two main topics of this book are Iwasawa theory and modular forms. The presentation of the theory of modular forms starts with several beautiful relations discovered by Ramanujan and leads to a discussion of several important ingredients, including the zeta-regularized products, Kronecker's limit formula, and the Selberg trace formula. The presentation of Iwasawa theory focuses on the Iwasawa main conjecture, which establishes far-reaching relations between a $p$-adic analytic zeta function and a determinant defined from a Galois action on some ideal class groups. This book also contains a short exposition on the arithmetic of elliptic curves and the proof of Fermat's last theorem by Wiles. Together with the first two volumes, this book is a good resource for anyone learning or teaching modern algebraic number theory.

Table of Contents

Contents Contents for number theory Contents for number theory Preface Preface to the English edition Objectives and outline of these books Modular forms Iwasawa theory Modular forms II Ellliptic curves II Bibliography Answers to questions Answers to exercises Index

by "Nielsen BookData"

Details

• NCID: BB10352967
• ISBN:
  • 9780821820957
• LCCN: 99033556
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Original Language Code: jpn
• Place of Publication: Providence, RI
• Pages/Volumes: xiv, 226 p.
• Size: 22 cm
• Classification:
  • LCC : QA241
  • DC21 : 512/.7
• Subject Headings:
  • LCSH : Number theory
• Parent Bibliography ID:
  • BA00080309
  • BA4365335X