Analytic methods for Diophantine equations and Diophantine inequalities. Edited and prepared by T. D. Browning. With a preface by R. C. Vaughan, D. R. Heath-Brown and D. E. Freeman. 2nd ed. (English) Zbl 1125.11018

Cambridge Mathematical Library. Cambridge: Cambridge University Press (ISBN 0-521-60583-0/pbk). xx, 140 p. (2005).
Publisher’s 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.
The original edition was published by Ann Arbor Publishers, Ann Arbor, Mich. in 1963.


11Dxx Diophantine equations
11-02 Research exposition (monographs, survey articles) pertaining to number theory
11P05 Waring’s problem and variants
11D72 Diophantine equations in many variables
11D79 Congruences in many variables
11D75 Diophantine inequalities
01A75 Collected or selected works; reprintings or translations of classics


Zbl 1089.11500