Synopses & Reviews
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 edition.
Synopsis
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.
Synopsis
This text investigates Waring's problem, approximation by fractional parts of the values of a polynomial, estimates for Weyl sums, distribution of fractional parts of polynomial values, Goldbach's problem, more. 1954 edition.
Table of Contents
I. General Lemmas
II. The Investigation of the Singular Series in Warings Problem
III. The Contribution of the Basic Intervals in Warings Problem
IV. An Estimate for G(n) in Warings Problem
V. Approximation by the Fractional Parts of the Values of a Polynomial
VI. Estimates for Weyl Sums
VII. The Asymptotic Formula in Warings Problem
VIII. The Distribution of the Fractional Parts of the Values of a Polynomial
IX. Estimates for the Simplest Trigonometrical Sums with Primes
X. Goldbachs Problem