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

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. Introduction: Fermat And Number Theory. -- Rational Points On Elliptic Curves. -- Conics And P-adic Numbers. -- [zeta Function] -- Algebraic Number Theory. -- Appendix A. Rudiments On Dedekind Domains. Kazuya Kato, Nobushige Kurokawa, Takeshi Saito ; Translated By Masato Kuwata. Includes Index. Translated From The Japanese.