Analytic Methods for Diophantine Equations and Diophantine Inequalities

Harold Davenport - Collection Cambridge Mathematical Library

140 pages, parution le 04/04/2005 (2^eme édition)

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Résumé

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.

Sommaire

Foreword
Editorial preface
Introduction
Waring's problem: history
Weyl's inequality and Hua's inequality
Waring's problem: the asymptotic formula
Waring's problem: the singular series
The singular series continued.
The equation C₁x^k₁ +...+ C_sx^k_s=N
The equation C₁x^k₁ +...+ C_sx^k_s=0
Waring's problem: the number G (k)
The equation C₁x^k₁ +...+ C_sx^k_s=0 again
General homoogeneous equations: Birch's theorem
The geometry of numbers
cubic forms
Cubic forms: bilinear equations
Cubic forms: minor arcs and major arcs
Cubic forms: the singular integral
Cubic forms: the singular series
Cubic forms: the p-adic problem
Homogeneous equations of higher degree
A Diophantine inequality
References
Index

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	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Harold Davenport
Collection	Cambridge Mathematical Library
Parution	04/04/2005
Édition	2^eme édition
Nb. de pages	140
Format	15 x 22,5
Couverture	Broché
Poids	260g
Intérieur	Noir et Blanc
EAN13	9780521605830
ISBN13	978-0-521-60583-0