Analytic Methods for Diophantine Equations and Diophantine Inequalities

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. 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.

"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