Translations of Mathematical Monographs
Iwanami Series in Modern Mathematics
2000;
154 pp;
Softcover
MSC: Primary 11; 14;
Print ISBN: 978-0-8218-0863-4
Product Code: MMONO/186
List Price: $37.00
AMS Member Price: $29.60
MAA Member Price: $33.30
Electronic ISBN: 978-1-4704-4600-0
Product Code: MMONO/186.E
List Price: $34.00
AMS Member Price: $27.20
MAA Member Price: $30.60
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Number Theory 1: Fermat’s Dream
Share this pageKazuya Kato; Nobushige Kurokawa; 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.
Readership
Graduate students and research mathematicians interested in number theory.
Reviews & Endorsements
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
Table of Contents
Number Theory 1: Fermat's Dream
- Cover Cover11
- Title page v6
- Contents vii8
- Preface ix10
- Preface to the English edition xi12
- Objectives and outline of these books xiii14
- Notation xv16
- Introduction 118
- Rational points on elliptic curves 1734
- Conics and 𝑝-adic numbers 4562
- 𝜁 8198
- Algebraic number theory 103120
- Rudiments on Dedekind domains 135152
- Answers to questions 139156
- Answers to exercises 145162
- Index 153170
- Back Cover Back Cover1174