Discriminant equations in diophantine number theory
Author(s)
Bibliographic Information
Discriminant equations in diophantine number theory
(New mathematical monographs, 32)
Cambridge University Press, 2017
Available at 8 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
-
Library, Research Institute for Mathematical Sciences, Kyoto University数研
EVE||7||3200035961784
Note
Includes bibliographical references (p. 440-453) and index
Description and Table of Contents
Description
Discriminant equations are an important class of Diophantine equations with close ties to algebraic number theory, Diophantine approximation and Diophantine geometry. This book is the first comprehensive account of discriminant equations and their applications. It brings together many aspects, including effective results over number fields, effective results over finitely generated domains, estimates on the number of solutions, applications to algebraic integers of given discriminant, power integral bases, canonical number systems, root separation of polynomials and reduction of hyperelliptic curves. The authors' previous title, Unit Equations in Diophantine Number Theory, laid the groundwork by presenting important results that are used as tools in the present book. This material is briefly summarized in the introductory chapters along with the necessary basic algebra and algebraic number theory, making the book accessible to experts and young researchers alike.
Table of Contents
- Preface
- Summary
- Part I. Preliminaries: 1. Finite etale algebras over fields
- 2. Dedekind domains
- 3. Algebraic number fields
- 4. Tools from the theory of unit equations
- Part II. Monic Polynomials and Integral Elements of Given Discriminant, Monogenic Orders: 5. Basic finiteness theorems
- 6. Effective results over Z
- 7. Algorithmic resolution of discriminant form and index form equations
- 8. Effective results over the S-integers of a number field
- 9. The number of solutions of discriminant equations
- 10. Effective results over finitely generated domains
- 11. Further applications
- Part III. Binary Forms of Given Discriminant: 12. A brief overview of the basic finiteness theorems
- 13. Reduction theory of binary forms
- 14. Effective results for binary forms of given discriminant
- 15. Semi-effective results for binary forms of given discriminant
- 16. Invariant orders of binary forms
- 17. On the number of equivalence classes of binary forms of given discriminant
- 18. Further applications
- Glossary of frequently used notation
- References
- Index.
by "Nielsen BookData"