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 inequalities. It provides an excellent introduction to a timeless area of number theory that is still as widely researched today as it was when the book originally appeared. The three main themes of the book are Waring's problem and the representation of integers by diagonal forms, the solubility in integers of systems of forms in many variables, and the solubility in integers of diagonal inequalities. For the second edition of the book a comprehensive foreword has been added in which three prominent authorities describe the modern context and recent developments. A thorough bibliography has also been added.
Rezensionen / Stimmen
"Analytic Methods stands on its own as yet another great example of Davenport's style and ability to present a number theory topic. Moreover, the new edition of his lecture notes include a foreword written by three experts...where the recent discoveries and state of the art on the topics covered in the book are summarized, adding a great amount to the total value of the volume."
MAA Reviews, Alvara Lozano-Robledo, Cornell University
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Sprache
Verlagsort
Zielgruppe
Produkt-Hinweis
Illustrationen
Worked examples or Exercises
Maße
Höhe: 229 mm
Breite: 152 mm
Dicke: 9 mm
Gewicht
ISBN-13
978-0-521-60583-0 (9780521605830)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Preface; Foreword; 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. The singular series continued; 7. The equation C1xk1 +...+ Csxks=N; 8. The equation C1xk1 +...+ Csxks=0; 9. Waring's problem: the number G (k); 10. The equation C1xk1 +...+ Csxks=0 again; 11. General homoogeneous equations: Birch's theorem; 12. The 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. A Diophantine inequality; Bibliography; Index.
