Softcover ISBN:  9780821820957 
Product Code:  MMONO/242 
List Price:  $53.00 
MAA Member Price:  $47.70 
AMS Member Price:  $42.40 
Electronic ISBN:  9780821891629 
Product Code:  MMONO/242.E 
List Price:  $53.00 
AMS Member Price:  $42.40 

Book DetailsTranslations of Mathematical MonographsIwanami Series in Modern MathematicsVolume: 242; 2012; 226 ppMSC: 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 zetaregularized products, Kronecker's limit formula, and the Selberg trace formula. The presentation of Iwasawa theory focuses on the Iwasawa main conjecture, which establishes farreaching 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.ReadershipGraduate students interested in number theory.

Table of Contents

Chapters

Modular forms

Iwasawa theory

Modular forms II

Ellliptic curves II


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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 zetaregularized products, Kronecker's limit formula, and the Selberg trace formula. The presentation of Iwasawa theory focuses on the Iwasawa main conjecture, which establishes farreaching 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.
Graduate students interested in number theory.

Chapters

Modular forms

Iwasawa theory

Modular forms II

Ellliptic curves II