The method of trigonometrical sums in the theory of numbers

I. M. Vinogradov0486438783, 9780486438788

This text begins with a discussion of general lemmas and advances to an investigation of Waring’s problem, including explorations of singular series, the contribution of the basic intervals, and an estimate for G(n). Further topics include approximation by the fractional parts of the values of a polynomial, estimates for Weyl sums, much more. 1954 edition.

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Table of contents :
Title page……Page 1
Title……Page 2
Date-line……Page 3
Preface by the Translators……Page 4
CONTENTS……Page 5
Notation……Page 7
Introduction……Page 9
Note on Vinogradov’s Method by the Translators……Page 27
I. General Lemmas……Page 29
Notes……Page 50
II. The Investigation of the Singular Series in Waring’s Problem……Page 53
Notes……Page 62
III. The Contribution of the Basic Intervals in Waring’s Problem……Page 63
Notes……Page 69
IV. An Estimate for G(n) in Waring’s Problem……Page 70
Notes……Page 77
V. Approximation by the Fractional Parts of the Values of a Polynomial……Page 79
Notes……Page 89
VI. Estimates for Weyl Sums……Page 90
Notes……Page 121
VII. The Asymptotic Formula in Waring’s Problem……Page 125
Notes……Page 131
VIII. The Distribution of the Fractional Parts of the Values of a Polynomial……Page 132
Notes……Page 135
IX. Estimates for the Simplest Trigonometrical Sums with Primes……Page 136
Notes……Page 170
X. Goldbach’s Problem……Page 171
Notes……Page 183
XI. The Distribution of the Fractional Parts of the Values of the Function cup……Page 185
Notes……Page 188