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

"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