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Analytic Methods for Diophantine Equations
and Diophantine Inequalities
Harold Davenport was one of the truly great mathematicians of the twen-
tieth 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 Diophan-
tine 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 prehensive foreword has been
added in which three leading experts describe the modern context and
recent developments. plete list of references has also been added.
Analytic Methods for Diophantine Equations
and Diophantine Inequalities
Second edition
H. Davenport
This edition edited and prepared for publication by
T. D. Browning
Oxford University
cambridge university press
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
Cambridge University Press
The Edinburgh Building, Cambridge cb2 2ru, UK
Published in the United States of America by Cambridge University Press, New York
Information on this title: 0521605830
© Estate of Harold Davenport 1963, 2005
This book is in copyright. Subject to statutory exception and to the provision of
relevant collective licensing agreements, no reproduction of any part may take place
without the written permission of Cambridge University Press.
First published in print format 2005
isbn-13 978-0-511-08086-9 eBook (NetLibrary)
isbn-10 0-511-08086-7 eBook (NetLibrary)
isbn-13 978-0-521-60583-0 paperback
isbn-10 0-521-60583-0 paperbac