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Analytic Methods for Diophantine Equations and Diophantine Inequalities


Part of Cambridge Mathematical Library

  • Date Published: March 2005
  • availability: Available
  • format: Paperback
  • isbn: 9780521605830

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About the Authors
  • 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.

    • A re-issue of a classic text
    • A comprehensive foreword has been added in which three prominent authorities describe the modern context and recent developments
    • A comprehensive bibliography and index has also been added
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    Product details

    • Date Published: March 2005
    • format: Paperback
    • isbn: 9780521605830
    • length: 160 pages
    • dimensions: 228 x 150 x 13 mm
    • weight: 0.26kg
    • availability: Available
  • Table of Contents

    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

  • Author

    H. Davenport

    Prepared for publication by

    T. D. Browning, University of Oxford

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