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Analytic methods for Diophantine equations and Diophantine inequalities /
"Harold Davenport was one of the truly great mathematicians of the twentieth century. Based on lectures he gave at the University of Michigan in the early 1960s, this book is concerned with the use of analytic methods in the study of integer solutions to Diophantine equations and Diophantine in...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge, UK ; New York :
Cambridge University Press,
2005.
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| Edición: | 2nd ed. |
| Colección: | Cambridge mathematical library.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Waring's problem / R.C. Vaughan
- Forms in many variables / D.R. Heath-Brown
- Diophantine inequalities / D.E. Freeman
- 1. Introduction
- 2. Waring's problem : history
- 3. Weyl's inequality and Hua's inequality
- 4. Waring's problem : the asymptotic formula
- 5. Waring's problem : the singular series
- 6. singular series continued
- 7. equation c[subscript 1]x[subscript 1][superscript k] + ... + c[subscript s]x[subscript s][superscript k] = N
- 8. equation c[subscript 1]x[subscript 1][superscript k] + ... + c[subscript s]x[subscript s][superscript k] = 0
- 9. Waring's problem : the number G(k)
- 10. equation c[subscript 1]x[subscript 1][superscript k] + ... + c[subscript s]x[subscript s][superscript k] = 0 again
- 11. General homogeneous equations : Birch's theorem
- 12. geometry of numbers
- 13. Cubic forms
- 14. Cubic forms : bilinear equations
- 15. Cubic forms : minor arcs and major arcs
- 16. Cubic forms : the singular integral
- 17. Cubic forms : the singular series
- 18. Cubic forms : the p-adic problem
- 19. Homogeneous equations of higher degree
- 20. Diophantine inequality.