Number Theory 3
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A01=Masato Kurihara
A01=Nobushige Kurokawa
A01=Takeshi Saito
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Author_Masato Kurihara
Author_Nobushige Kurokawa
Author_Takeshi Saito
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Product details
- ISBN 9780821820957
- Weight: 280g
- Publication Date: 30 Oct 2012
- Publisher: American Mathematical Society
- Publication City/Country: US
- Product Form: Paperback
- Language: English
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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 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.
Nobushige Kurokawa, Tokyo Institute of Technology, Tokyo, Japan,
Masato Kurihara, Keio University, Yokohama, Japan,
Takeshi Saito, University of Tokyo, Tokyo, Japan
Masato Kurihara, Keio University, Yokohama, Japan,
Takeshi Saito, University of Tokyo, Tokyo, Japan
