The Hardy-Littlewood Method

Cambridge Tracts in Mathematics #125

by R.C. Vaughan

The Hardy-Littlewood method is a means of estimating the number of integer solutions of equations and was first applied to Waring's problem on representations of integers by sums of powers. This introduction to the method deals with its classical forms and outlines some of the more recent developments. Now in its second edition it has been fully updated; the author has made extensive revisions and added a new chapter to take account of major advances by Vaughan and Wooley. The reader is expected to be familiar with elementary number theory and postgraduate students should find it of great use as an advanced textbook. It will also be indispensable to all lecturers and research workers interested in number theory.

248 pages, Hardcover

First published January 1, 1981

Reviews

[Sam Chow · Rating 3 out of 5]

This is an excellent reference book, and it is essential for an additive number theorist to know what is here. Many of the results are still state of the art, though many long for a new book to be written. Still, anyone who has commenced learning the circle method via this book will describe the countless hours of pain that they had to endure. This is possibly a fair warning to would-be circle-methodists, though many tell of more efficient ways in which to learn the circle method, and they are probably right (I wouldn't know. Consider for instance Davenport's "Analytic methods for Diophantine Equations and Diophantine inequalities...). The student should probably learn some general analytic number theory first, and I also refer to Browning's "Quantitative arithmetic of projective varieties" for a broader perspective. Think of Vaughan's book as a neat summary.