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Iwanami Series in Modern Mathematics
Number Theory 1: Fermat's Dream
Kazuya Kato, University of Tokyo, Japan, Nobushige Kurokawa, Tokyo Institute of Technology, Japan, and Takeshi Saito, University of Tokyo, Japan

Translations of Mathematical Monographs
Iwanami Series in Modern Mathematics
2000; 154 pp; softcover
Volume: 186
ISBN-10: 0-8218-0863-X
ISBN-13: 978-0-8218-0863-4
List Price: US$34
Member Price: US$27.20
Order Code: MMONO/186
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See also:

Number Theory 2: Introduction to Class Field Theory - Kazuya Kato, Nobushige Kurokawa and Takeshi Saito

Number Theory 3: Iwasawa Theory and Modular Forms - Nobushige Kurokawa, Masato Kurihara and Takeshi Saito

This is the English translation of the original Japanese book. In this volume, "Fermat's Dream", core theories in modern number theory are introduced. Developments are given in elliptic curves, \(p\)-adic numbers, the \(\zeta\)-function, and the number fields. This work presents an elegant perspective on the wonder of numbers. Number Theory 2 on class field theory, and Number Theory 3 on Iwasawa theory and the theory of modular forms, are forthcoming in the series.

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Graduate students and research mathematicians interested in number theory.


"This book can be recommended to any scholar or student having the required background; in particular, it would make excellent supplementary reading for students having taken a first course in number theory. The text would also constitute a good basis for lectures to an audience of nonspecialists."

-- Mathematical Reviews

Table of Contents

  • Introduction
  • Rational points on elliptic curves
  • Conics and \(p\)-adic numbers
  • \(\zeta\)
  • Algebraic number theory
  • Rudiments on Dedekind domains
  • Answers to questions
  • Answers to exercises
  • Index
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