Number Theory 1 :Fermat's Dream ( Translations of Mathematical Monographs )

Publication subTitle :Fermat's Dream

Publication series : Translations of Mathematical Monographs

Author: Kazuya Kato;Nobushige Kurokawa;Takeshi Saito  

Publisher: American Mathematical Society‎

Publication year: 2018

E-ISBN: 9781470446000

P-ISBN(Paperback): 9780821808634

Subject: O156 Number Theory

Keyword: 数学

Language: ENG

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Number Theory 1

Description

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.

Chapter

Title page

Contents

Preface

Preface to the English edition

Objectives and outline of these books

Notation

Introduction

Rational points on elliptic curves

Conics and 𝑝-adic numbers

𝜁

Algebraic number theory

Rudiments on Dedekind domains

Answers to questions

Answers to exercises

Index

Back Cover

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