The Method Of Trigonometric Sums In The Theory Of Numbers – Vinogradov

In this post, we will see the book The Method Of Trigonometric Sums In The Theory Of Numbers by I. M. Vinogradov.

About the book

Since 1934 the analytic theory of numbers has been largely transformed by the work of Vinogradov. This work, which has led to remarkable new 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, which appeared in 1937 and 1947. The present book is a translation of the second of these monographs, which incorporated the improvements effected by the author during the intervening ten years.

The text has been carefully revised and to some extent rewritten. The more difficult arguments have been set out in greater detail.

Notes have been added, in which we mention the more im­portant changes made and comment on the subject-matter; we hope these will be of assistance or of interest to the reader.

The book was translated from Russian by K. F. Roth and Anne Davenport and was published in 1954.

Credits to the original uploader.

You can get the book here.

Follow us on The Internet Archive: https://archive.org/details/@mirtitles

Follow Us On Twitter: https://twitter.com/MirTitles

Write to us: mirtitles@gmail.com

Fork us at GitLab: https://gitlab.com/mirtitles/

Add new entries to the detailed book catalog here.

Contents

Preface by the Translators V
Notation ix

Introduction 1

Note on Vinogradov’s Method by the Translators 19

I. General Lemmas 21

Notes 42

II. The Investigation of the Singular Series in Waring’s Problem 45

Notes 54

III. The Contribution of the Basic Intervals in Waring’s Problem 55

Notes 61

IV. An Estimate for G(n) in Waring’s Problem 62

Notes 69

V. Approximation by the Fractional Parts of the Values of a Polynomial 71

Notes 81

VI. Estimates for Weyl Sums 82

Notes 113

VII. The Asymptotic Formula in Waring’s Problem 117

Notes 123

VIII. The Distribution of the Fractional Parts of the Values of a Polynomial 124

Notes 127

IX. Estimates for the Simplest Trigonometrical Sums with Primes 128

Notes 162

X. Goldbach’s Problem 163

Notes 175

XI. The Distribution of the Fractional Parts of the Values of the Function 𝛼𝓅 177

Notes 180

About The Mitr

I am The Mitr, The Friend
This entry was posted in mathematics, soviet and tagged , , , , , , , , . Bookmark the permalink.

1 Response to The Method Of Trigonometric Sums In The Theory Of Numbers – Vinogradov

  1. Pingback: The Method Of Trigonometric Sums In The Theory Of Numbers – Vinogradov | Chet Aero Marine

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.