The Method of Trigonometrical Sums in the Theory of Numbers

by I. M. Vinogradov

Overview

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.

Product Details

ISBN-13:	9780486154527
Publisher:	Dover Publications
Publication date:	10/30/2013
Series:	Dover Books on Mathematics
Sold by:	Barnes & Noble
Format:	eBook
Pages:	192
File size:	17 MB
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Table of Contents

I. General Lemmas
II. The Investigation of the Singular Series in Waring’s Problem
III. The Contribution of the Basic Intervals in Waring’s Problem
IV. An Estimate for G(n) in Waring’s Problem
V. Approximation by the Fractional Parts of the Values of a Polynomial
VI. Estimates for Weyl Sums
VII. The Asymptotic Formula in Waring’s Problem
VIII. The Distribution of the Fractional Parts of the Values of a Polynomial
IX. Estimates for the Simplest Trigonometrical Sums with Primes
X. Goldbach’s Problem