© 1990

An Introduction to Algebraic Number Theory


Part of the University Series in Mathematics book series (USMA)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Takashi Ono
    Pages 1-43
  3. Takashi Ono
    Pages 105-142
  4. Back Matter
    Pages 195-223

About this book


This book is a translation of my book Suron Josetsu (An Introduction to Number Theory), Second Edition, published by Shokabo, Tokyo, in 1988. The translation is faithful to the original globally but, taking advantage of my being the translator of my own book, I felt completely free to reform or deform the original locally everywhere. When I sent T. Tamagawa a copy of the First Edition of the original work two years ago, he immediately pointed out that I had skipped the discussion of the class numbers of real quadratic fields in terms of continued fractions and (in a letter dated 2/15/87) sketched his idea of treating continued fractions without writing explicitly continued fractions, an approach he had first presented in his number theory lectures at Yale some years ago. Although I did not follow his approach exactly, I added to this translation a section (Section 4. 9), which nevertheless fills the gap pointed out by Tamagawa. With this addition, the present book covers at least T. Takagi's Shoto Seisuron Kogi (Lectures on Elementary Number Theory), First Edition (Kyoritsu, 1931), which, in turn, covered at least Dirichlet's Vorlesungen. It is customary to assume basic concepts of algebra (up to, say, Galois theory) in writing a textbook of algebraic number theory. But I feel a little strange if I assume Galois theory and prove Gauss quadratic reciprocity.


Galois theory algebra algebraic number theory number theory

Authors and affiliations

  1. 1.The Johns Hopkins University BaltimoreBaltimoreUSA

Bibliographic information

  • Book Title An Introduction to Algebraic Number Theory
  • Authors Takashi Ono
  • Series Title University Series in Mathematics
  • DOI
  • Copyright Information Springer-Verlag US 1990
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-306-43436-5
  • Softcover ISBN 978-1-4612-7872-6
  • eBook ISBN 978-1-4613-0573-6
  • Edition Number 1
  • Number of Pages XI, 223
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Algebra
  • Buy this book on publisher's site