The algorithmic resolution of diophantine equations
Author(s)
Bibliographic Information
The algorithmic resolution of diophantine equations
（London Mathematical Society student texts, v. 41）
Cambridge University Press, 1998
- : hard
- : pbk
Available at / 53 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
: hardSMA||5||198054158
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The University of Electro-Communications Library研
: pbk.412.9/Sm2,412.4/Sm22219806555,2003103686
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC21:510/Sm292070453921
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Note
Includes bibliographical references (p. 231-239) and index
Description and Table of Contents
Description
Beginning with a brief introduction to algorithms and diophantine equations, this volume aims to provide a coherent account of the methods used to find all the solutions to certain diophantine equations, particularly those procedures which have been developed for use on a computer. The study is divided into three parts, the emphasis throughout being on examining approaches with a wide range of applications. The first section considers basic techniques including local methods, sieving, descent arguments and the LLL algorithm. The second section explores problems which can be solved using Baker's theory of linear forms in logarithms. The final section looks at problems associated with curves, mainly focusing on rational and integral points on elliptic curves. Each chapter concludes with a useful set of exercises. A detailed bibliography is included. This book will appeal to graduate students and research workers, with a basic knowledge of number theory, who are interested in solving diophantine equations using computational methods.
Table of Contents
- Preface
- 1. Introduction
- Part I. Basic Solution Techniques: 2. Local methods
- 3. Applications of local methods to diophantine equations
- 4. Ternary quadratic forms
- 5. Computational diophantine approximation
- 6. Applications of the LLL-algorithm
- Part II. Methods Using Linear Forms in Logarithms: 7. Thue equations
- 8. Thue-Mahler equations
- 9. S-Unit equations
- 10. Triangularly connected decomposable form equations
- 11. Discriminant form equations
- Part III. Integral and Rational Points on Curves: 12. Rational points on elliptic curves
- 13. Integral points on elliptic curves
- 14. Curves of genus greater than one
- Appendices
- References
- Index.
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