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.
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Editorial Reviews
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"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 --This text refers to the Paperback edition.
MAA Reviews, Alvara Lozano-Robledo, Cornell University --This text refers to the Paperback edition.
Book Description
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.
--This text refers to the
Paperback
edition.
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Key Phrases - Statistically Improbable Phrases (SIPs):
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positive integral kth powers, mod pry, equation clxl, general homogeneous equations, singular series, major arcs, bilinear equations, minor arcs, congruence conditions, successive minima, integer points, asymptotic formula, cubic forms, positive lower bound, trivial estimate Key Phrases - Capitalized Phrases (CAPs): (learn more)
Diophantine Equations Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
positive integral kth powers, mod pry, equation clxl, general homogeneous equations, singular series, major arcs, bilinear equations, minor arcs, congruence conditions, successive minima, integer points, asymptotic formula, cubic forms, positive lower bound, trivial estimate Key Phrases - Capitalized Phrases (CAPs): (learn more)
Diophantine Equations Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
Citations (learn more)
4
books
cite this book:
- Tha(c)Orie Des Nombres / Number Theory: Proceedings of the International Number Theory Conference Held at Universita(c) Laval, July 5-18, 1987 ([De ... Proceedings in Mathematics]) (French Edition) by Claude Levesque on page 733
- Selected Papers Of Wang Yuan by Wang Yuan on page 287
- Additive Number Theory The Classical Bases (Graduate Texts in Mathematics) by Melvyn B. Nathanson in Back Matter
- Multiplicative Number Theory I: Classical Theory (Cambridge Studies in Advanced Mathematics) by Hugh L. Montgomery on page 33
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