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.

The original edition was published by Ann Arbor Publishers, Ann Arbor, Mich. in 1963.

##### MSC:

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 |