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Method of Trigonometrical Sums in the Theory of Numbers

โœ Scribed by Vinogradov I.M.

Book ID
127449515
Year
2004
Tongue
English
Weight
3 MB
Category
Library

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โœฆ Synopsis

Since the 1930s, the analytic theory of numbers has been transformed by the influence of I. M. Vinogradov. The Method of Trigonometrical Sums in the Theory of Numbers, which led to remarkable new results, testifies to its author's supreme ingenuity and to the effectiveness of his methods. Starting with a discussion of general lemmas, the text advances to an investigation of Waring's problem, including explorations of the 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. Recent research on the type of problems studied by Vinogradov indicates that his methods remain among the most powerful. This text will prove of enormous benefit to upper-level undergraduates and graduate students.

๐Ÿ“œ SIMILAR VOLUMES

The method of trigonometrical sums in th
The method of trigonometrical sums in the theory of numbers
โœ I. M. Vinogradov ๐Ÿ“‚ Library ๐Ÿ“… 2004 ๐Ÿ› Dover Publications ๐ŸŒ English โš– 1 MB

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 p

Trigonometric sums in number theory and
Trigonometric sums in number theory and analysis
โœ G. I. Arkhipov, V. N. Chubarikov, A. A. Karatsuba, Gennadii Ivanovich Arkhipov, ๐Ÿ“‚ Library ๐Ÿ“… 2004 ๐Ÿ› Walter de Gruyter ๐ŸŒ English โš– 3 MB

The book presents the theory of multiple trigonometric sums constructed by the authors. Following a unified approach, the authors obtain estimates for these sums similar to the classical I. M. Vinogradov's estimates and use them to solve several problems in analytic number theory. They investigate t

Trigonometric Sums in Number Theory and
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โœ G. I. Arkhipov, V. N. Chubarikov, A. A. Karatsuba, Gennadii Ivanovich Arkhipov, ๐Ÿ“‚ Library ๐Ÿ“… 2004 ๐Ÿ› Walter de Gruyter ๐ŸŒ English โš– 3 MB

Vinogradov first developed the method of trigonometric sums in the first decades of the twentieth century as a way of solving problems in analytical number theory. The authors here present a systematic account of the theory of multiple trigonometric sums, using a unified approach to derive results s