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The Method of Trigonometrical Sums in the Theory of Numbers (Dover Books on Mathematics)

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Since 1934 the analytic theory of numbers has been largely transformed by the \vork of Vinogradov. This \vork, which has led to remarkable ne\v results, is characterized by its supreme ingenuity and great power.

Vinogradov has expounded his method and its applications in a series of papers and in two monographs 1), which appeared in 1937 and 1947. The present book is a translation of the second  of these monographs, vvhich incorporated the improvements effectedby the author during the intervening ten years.

The text has been carefully revised and to some extent re\vritten. The more difficult arguments have been set out in greater detail.  Notes have been added, in which we mention the more importantchanges made and comment on the subject-matter;

we hope these will be of assistance or of interest to the read( 'f.In particular, in the Kotes on Chapter VI, we mention a simplification effected by Hua in 1948.

We are greatly indebted to Professor Davenport, who has given substantial help throughout. We are also grateful to Professor l\iordell and to Dr. G. L. Watson for a number of helpful comments.
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