**Translations of Mathematical Monographs
Iwanami Series in Modern Mathematics**

2012; 226 pp; Softcover

MSC: Primary 11;

**Print ISBN: 978-0-8218-2095-7**

Product Code: MMONO/242

Product Code: MMONO/242

List Price: $53.00

AMS Member Price: $42.40

MAA Member Price: $47.70

**Electronic ISBN: 978-0-8218-9162-9
Product Code: MMONO/242.E**

List Price: $53.00

AMS Member Price: $42.40

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# Number Theory 3: Iwasawa Theory and Modular Forms

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*Nobushige Kurokawa; Masato Kurihara; Takeshi Saito*

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.

#### Readership

Graduate students interested in number theory.

#### Table of Contents

# Table of Contents

## Number Theory 3: Iwasawa Theory and Modular Forms

- Cover Cover11
- Title page i2
- Contents iii4
- Contents for number theory 2 v6
- Contents for number theory 1 vii8
- Preface ix10
- Preface to the English edition xi12
- Objectives and outline of these books xiii14
- Modular forms 116
- Iwasawa theory 87102
- Modular forms II 167182
- Ellliptic curves II 189204
- Bibliography 211226
- Answers to questions 217232
- Answers to exercises 219234
- Index 225240
- Back Cover Back Cover1242