Iwasawa theory and modular forms
著者
書誌事項
Iwasawa theory and modular forms
（Translations of mathematical monographs, v. 242 . Number theory ; 3）（Iwanami series in modern mathematics）
American Mathematical Society, c2012
- タイトル別名
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数論. 3 : 岩澤理論と保型形式
Sūron
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注記
"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
内容説明・目次
内容説明
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.
目次
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
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