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Number Theory 3: Iwasawa Theory and Modular Forms

Nobushige Kurokawa Tokyo Institute of Technology, Tokyo, Japan
Masato Kurihara Keio University, Yokohama, Japan
Takeshi Saito University of Tokyo, Tokyo, Japan
Available Formats:
Softcover ISBN: 978-0-8218-2095-7
Product Code: MMONO/242
List Price: $53.00 MAA Member Price:$47.70
AMS Member Price: $42.40 Electronic ISBN: 978-0-8218-9162-9 Product Code: MMONO/242.E List Price:$53.00
AMS Member Price: $42.40 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$79.50
MAA Member Price: $71.55 AMS Member Price:$63.60
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Number Theory 3: Iwasawa Theory and Modular Forms
Nobushige Kurokawa Tokyo Institute of Technology, Tokyo, Japan
Masato Kurihara Keio University, Yokohama, Japan
Takeshi Saito University of Tokyo, Tokyo, Japan
Available Formats:
 Softcover ISBN: 978-0-8218-2095-7 Product Code: MMONO/242
 List Price: $53.00 MAA Member Price:$47.70 AMS Member Price: $42.40  Electronic ISBN: 978-0-8218-9162-9 Product Code: MMONO/242.E  List Price:$53.00 AMS Member Price: $42.40 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$79.50 MAA Member Price: $71.55 AMS Member Price:$63.60
• Book Details

Translations of Mathematical Monographs
Iwanami Series in Modern Mathematics
Volume: 2422012; 226 pp
MSC: Primary 11;

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

• Chapters
• Modular forms
• Iwasawa theory
• Modular forms II
• Ellliptic curves II
• Additional Material

• Requests

Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Iwanami Series in Modern Mathematics
Volume: 2422012; 226 pp
MSC: Primary 11;

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.

• Chapters
• Modular forms
• Iwasawa theory
• Modular forms II
• Ellliptic curves II
Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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