The Algorithmic Resolution of Diophantine Equations

Klappentext A coherent account of the computational methods used to solve diophantine equations. Zusammenfassung A coherent account of the computational methods used to solve diophantine equations. Topics include local methods! sieving! descent arguments! the LLL algorithm! Baker's theory of linear forms in logarithms! and problems associated with curves. Useful exercises and bibliography are included. Suitable for graduate students and research workers. Inhaltsverzeichnis 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.

Klappentext
A coherent account of the computational methods used to solve diophantine equations.

Inhalt
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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