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数论中的三角和方法/The method of trigonometrical sums in the theory of numbers

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数论中的三角和方法/The method of trigonometrical sums in the theory of numbers

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作 者:I. M. Vinogradov 著

出 版 社:Oversea Publishing House

出版时间:2004-9-1

I S B N:9780486438788

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内容简介

Since the 1930s, the analytic theory of numbers has been transformed by the influence of I. M. Vinogradov, and this text for upper-level undergraduates and graduate students testifies to its author's ingenuity and to the effectiveness of his methods. Starting with a discussion of general lemmas, it 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, the asymptotic formula in Waring's problem, the distribution of the fractional parts of the values of a polynomial, estimates for the simplest trigonometrical sums with primes, and Goldbach's problem. 1954 ed.

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目录

Preface by the Translstors
Notation
Introduction
I.General Lemmas
II.The Investigation of the Singular Series inWaring’s Problem
III.The Contribution of the Basic Intervals inWaring’s Problem
IV.An Estimate for G(n) in Waring’s Problem
V.Approximation by the Fractional Parts of theValues 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 Notes
XI.The Distribution of the Fractional Parts of the Values of the Funstion ap
Notes

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