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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
Number Theory 3
Softcover ISBN:  978-0-8218-2095-7
Product Code:  MMONO/242
List Price: $52.00
MAA Member Price: $46.80
AMS Member Price: $41.60
eBook ISBN:  978-0-8218-9162-9
Product Code:  MMONO/242.E
List Price: $49.00
AMS Member Price: $39.20
Softcover ISBN:  978-0-8218-2095-7
eBook: ISBN:  978-0-8218-9162-9
Product Code:  MMONO/242.B
List Price: $101.00 $76.50
MAA Member Price: $68.85
AMS Member Price: $80.80 $61.20
Number Theory 3
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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
Softcover ISBN:  978-0-8218-2095-7
Product Code:  MMONO/242
List Price: $52.00
MAA Member Price: $46.80
AMS Member Price: $41.60
eBook ISBN:  978-0-8218-9162-9
Product Code:  MMONO/242.E
List Price: $49.00
AMS Member Price: $39.20
Softcover ISBN:  978-0-8218-2095-7
eBook ISBN:  978-0-8218-9162-9
Product Code:  MMONO/242.B
List Price: $101.00 $76.50
MAA Member Price: $68.85
AMS Member Price: $80.80 $61.20
  • 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 publishers of book reviews
    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 publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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